I took problematic computer to which this printer connected usually and checked it. The problem with it still is:

tail -f /var/log/syslog
Sep 25 14:05:12 Desktop kernel: [  564.333384] usblp0: removed
Sep 25 14:05:12 Desktop kernel: [  564.346921] usblp 2-1:1.0: usblp0: USB Bidirectional printer dev 3 if 0 alt 0 proto 2 vid 0x04E8 pid 0x300E
Sep 25 14:05:12 Desktop hp[1919]: io/hpmud/pp.c 627: unable to read device-id ret=-1
Sep 25 14:05:12 Desktop python: io/hpmud/pp.c 627: unable to read device-id ret=-1
Sep 25 14:05:12 Desktop udev-configure-printer: URI matches without serial number: usb://Samsung/ML-1250
Sep 25 14:05:12 Desktop udev-configure-printer: No serial number URI matches so using those without
Sep 25 14:05:12 Desktop udev-configure-printer: URI of detected printer: usb://Samsung/ML-1250, normalized: samsung ml 1250
Sep 25 14:05:12 Desktop udev-configure-printer: URI of print queue: usb://Samsung/ML-1250, normalized: samsung ml 1250
Sep 25 14:05:12 Desktop udev-configure-printer: Queue ipp://localhost:631/printers/Samsung-ML-1250 has matching device URI
Sep 25 14:05:12 Desktop udev-configure-printer: Re-enabled printer ipp://localhost:631/printers/Samsung-ML-1250
Sep 25 14:05:45 Desktop kernel: [  598.140368] usblp0: removed
Sep 25 14:05:58 Desktop kernel: [  610.321546] usblp 2-1:1.0: usblp0: USB Bidirectional printer dev 3 if 0 alt 0 proto 2 vid 0x04E8 pid 0x300E
Sep 25 14:05:58 Desktop kernel: [  610.321822] usblp0: removed
Sep 25 14:05:58 Desktop kernel: [  610.432036] usb 2-1: reset full-speed USB device number 3 using uhci_hcd
Sep 25 14:05:58 Desktop kernel: [  610.552031] usb 2-1: device descriptor read/64, error -71
Sep 25 14:05:58 Desktop kernel: [  610.776036] usb 2-1: device descriptor read/64, error -71
Sep 25 14:05:58 Desktop kernel: [  610.992021] usb 2-1: reset full-speed USB device number 3 using uhci_hcd
Sep 25 14:05:58 Desktop kernel: [  611.112036] usb 2-1: device descriptor read/64, error -71
Sep 25 14:05:59 Desktop kernel: [  611.336032] usb 2-1: device descriptor read/64, error -71
Sep 25 14:05:59 Desktop kernel: [  611.552022] usb 2-1: reset full-speed USB device number 3 using uhci_hcd
Sep 25 14:05:59 Desktop kernel: [  611.960022] usb 2-1: device not accepting address 3, error -71
Sep 25 14:05:59 Desktop kernel: [  612.072035] usb 2-1: reset full-speed USB device number 3 using uhci_hcd
Sep 25 14:06:00 Desktop kernel: [  612.484024] usb 2-1: device not accepting address 3, error -71
Sep 25 14:06:00 Desktop kernel: [  612.484126] usblp: can't set desired altsetting 0 on interface 0
Sep 25 14:06:00 Desktop kernel: [  612.485466] usb 2-1: USB disconnect, device number 3
Sep 25 14:06:00 Desktop udev-configure-printer: remove /devices/pci0000:00/0000:00:1d.0/usb2/2-1
Sep 25 14:06:00 Desktop udev-configure-printer: URI of detected printer: usb://Samsung/ML-1250, normalized: samsung ml 1250
Sep 25 14:06:00 Desktop udev-configure-printer: URI of print queue: usb://Samsung/ML-1250, normalized: samsung ml 1250
Sep 25 14:06:00 Desktop udev-configure-printer: Queue ipp://localhost:631/printers/Samsung-ML-1250 has matching device URI
Sep 25 14:06:00 Desktop udev-configure-printer: Disabled printer ipp://localhost:631/printers/Samsung-ML-1250 as the corresponding device was unplugged or turned off
Sep 25 14:06:00 Desktop kernel: [  612.596034] usb 2-1: new full-speed USB device number 4 using uhci_hcd
Sep 25 14:06:00 Desktop kernel: [  612.717264] usb 2-1: device descriptor read/64, error -71
Sep 25 14:06:00 Desktop kernel: [  612.940020] usb 2-1: device descriptor read/64, error -71
Sep 25 14:06:00 Desktop kernel: [  613.156074] usb 2-1: new full-speed USB device number 5 using uhci_hcd
Sep 25 14:06:00 Desktop kernel: [  613.276028] usb 2-1: device descriptor read/64, error -71
Sep 25 14:06:01 Desktop kernel: [  613.500033] usb 2-1: device descriptor read/64, error -71
Sep 25 14:06:01 Desktop kernel: [  613.717959] usb 2-1: new full-speed USB device number 6 using uhci_hcd
Sep 25 14:06:01 Desktop kernel: [  614.128031] usb 2-1: device not accepting address 6, error -71
Sep 25 14:06:01 Desktop kernel: [  614.240033] usb 2-1: new full-speed USB device number 7 using uhci_hcd
Sep 25 14:06:02 Desktop kernel: [  614.648024] usb 2-1: device not accepting address 7, error -71
Sep 25 14:06:02 Desktop kernel: [  614.648069] usb usb2-port1: unable to enumerate USB device

Interesting thing that earlier this issue was also when I checked this printer with other computers.