I have found a solution that works to fix the missing Analogs for me.  The solution is based on the information provided in PulseAudio ticket #624 here: http://pulseaudio.org/ticket/624 .

My card is the Delta 1010LT.  From my understanding of the ICE1712 cards they are all the same internally, just the input/output connectors are different from card to card.  I am running Ubuntu Karmic-rc so my installed versions of pulseaudio, udev, alsa, etc... are compatible with the fix described in PA ticket #624.

Here is a summary of what I learned from #624:
The ICE1712 card is properly recognized by alsa, its configuration is in "/usr/share/alsa/cards/ICE1712.conf".  This file is basically a default asound.conf for the card shipped with alsa.  

When pulseaudio is started it attempts to create profiles for the card each of which specifies how the card's inputs and outputs will be mapped.  Unfortunately pulseaudio is not currently able to auto-generate any profiles that support use of the card's analog inputs and outputs.  To fix this, the auto-generation of the profiles must be replaced for this card with some static profile definitions.  Two modifications need to be made to accomplish this: 1) addition of a udev rule to match the ICE1712 card; 2) a static ICE1712 profile definitions file

1) Create the new udev rule in "/lib/udev/rules.d/90-pulseaudio.rules".  Here is the rule I added to the file to detect my 1010LT:
SUBSYSTEMS=="pci", ATTRS{vendor}=="0x1412", ATTRS{device}=="0x1712", ENV{PULSE_PROFILE_SET}="via-ice1712.conf"

The above rule is generic enough to match any pci card with the ICE1712 chipset.  It defines a value for "PULSE_PROFILE_SET" that contains the name of the static profile definition to use with the card.

2) Create the static profile definition file "/usr/share/pulseaudio/alsa-mixer/profile-sets/via-ice1712.conf".  I initially copied the file exactly from ticket #624 attachments.  However I later made two modifications to the file for my own purposes to allow separate simultaneous use of each of the 1010LT's analog outputs and to map inputs 3&4 to front-left and front-right.  My mods can be seen in the sections entitled "[Mapping analog-mch-in]" and "[Mapping analog-mch-out]".

#### Begin via-ice1712.conf ####
# This file is part of PulseAudio.
#
# PulseAudio is free software; you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as
# published by the Free Software Foundation; either version 2.1 of the
# License, or (at your option) any later version.
#
# PulseAudio is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with PulseAudio; if not, write to the Free Software Foundation,
# Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.

; Via ICE1712 multi-channel audio chipset
;
; This chipset has up to four stereo pairs of input and four stereo pairs of
; output, named channels 1 to 8. Also available are separate S/PDIF stereo
; channels (input and output), and a separate "system-out" stereo jack that
; supports 6-channel hardware mixing.
;
; The S/PDIF stereo channels can be controlled via the mixer for hw:0, and
; additionally, the 8 main outputs can be loop-routed to a separate stereo
; input pair, available as channels 11 and 12.
;
; Many cards available from vendors do not expose all channels from this chip
; to an external port, which effectively reduces the number of channels that
; are useful to the user. However, the ALSA driver still exposes all channels
; even if they are not connected.
;
; We knowingly only define a subset of the theoretically possible
; mapping combinations as profiles here.
;
; See default.conf for an explanation on the directives used here.

[General]
auto-profiles = no

[Mapping analog-mch-in]
description = Analog Multi-Channel Main Input
device-strings = hw:%f,0
#channel-map = front-left,front-right,rear-left,rear-right,front-center,lfe,side-left,side-right,aux0,aux1,aux2,aux3
channel-map = aux0,aux1,front-left,front-right,aux2,aux3,aux4,aux5,aux6,aux7,aux8,aux9
direction = input

[Mapping analog-mch-out]
description = Analog Multi-Channel Main Output
device-strings = hw:%f,0
#channel-map = front-left,front-right,rear-left,rear-right,front-center,lfe,side-left,side-right,aux0,aux1
channel-map = front-left,front-right,aux0,aux1,aux2,aux3,aux4,aux5,aux6,aux7
direction = output

[Mapping digital-stereo]
description = Digital Stereo Input/Output
#device-strings = hw:%f,1
device-strings = iec958:%f
channel-map = left,right
direction = any

[Mapping analog-system-out]
description = Analog Stereo System-Out
device-strings = hw:%f,2
channel-map = left,right
direction = output


[Profile output:mch]
description = Multi-Channel Output Active (Digital Disabled)
output-mappings = analog-mch-out analog-system-out
input-mappings =
priority = 90
skip-probe = yes

[Profile output:mch+input:mch]
description = Multi-Channel Input/Output (Digital Disabled)
output-mappings = analog-mch-out analog-system-out
input-mappings = analog-mch-in
priority = 100
skip-probe = yes

[Profile output:spdif]
description = Digital Output (Multi-Channel Disabled)
output-mappings = digital-stereo analog-system-out
input-mappings =
priority = 80
skip-probe = yes

[Profile output:spdif+input:spdif]
description = Digital Input/Output (Multi-Channel Disabled)
output-mappings = digital-stereo analog-system-out
input-mappings = digital-stereo
priority = 90
skip-probe = yes

[Profile output:system]
description = System Output Only
output-mappings = analog-system-out
input-mappings =
priority = 60
skip-probe = yes
#### End via-ice1712.conf ####

As mentioned above I needed to use the analog outputs separately, so I performed a 3rd step to facilitate this.  In my "/etc/pulse/default.pa" I remapped the 8 analog outputs into 4 sinks, each a 2-channel mono output like this (note that my master sink names are unique to my hardware configuration and will likely not work for others):
# Map the 1010LT analog outputs
# break the outputs up into separate left/right channels
load-module module-remap-sink sink_name=mixer_5 master=alsa_output.pci-0000_03_06.0.analog-mch-out channels=2 master_channel_map=front-left,front-right channel_map=mono,mono
update-sink-proplist mixer_5 device.description="Mixer Channel 5"

load-module module-remap-sink sink_name=mixer_6 master=alsa_output.pci-0000_03_06.0.analog-mch-out channels=2 master_channel_map=aux0,aux1 channel_map=mono,mono
update-sink-proplist mixer_6 device.description="Mixer Channel 6"

load-module module-remap-sink sink_name=amp_3 master=alsa_output.pci-0000_03_06.0.analog-mch-out channels=2 master_channel_map=aux2,aux3 channel_map=mono,mono
update-sink-proplist amp_3 device.description="Amp Source 3"

load-module module-remap-sink sink_name=amp_4 master=alsa_output.pci-0000_03_06.0.analog-mch-out channels=2 master_channel_map=aux4,aux5 channel_map=mono,mono
update-sink-proplist amp_4 device.description="Amp Source 4"

From ticket #624 it looks like this change to the ICE1712 card profiles will be coming in a future version of pulseaudio.  In the meantime maybe my experience can help some folks to get their cards working with pulseaudio.