Mine has started doing this recently, now that I am using it for longer periods of time per session because have also started using the Helix as a USB out from my PC so I can play music and movies through my studio monitors. It does this after maybe 4-5 hours of the unit being powered-on. I can also hear a quiet burst of static through my studio monitors in time with the LED flash. I turn off the power switch off for a while, and then it resets itself and is okay again - however, this is not a short amount of time (it would be the end of any gig) and attempting to power the unit back on too soon just results in the flashing EXP lights.
Actively using the Helix and changing presents, etc., or simply turning it on and letting the unit idle doesn't matter - both will reproduce after the same 4-5 hours. Mine was originally 2.80 when the issue started, but updating to 2.82 didn't change anything.
I assumed it was some sort of overheat, but the unit is still completely cool to the touch all over, and it's not enclosed in a unit or sat on carpet or anything like that anyway, so an overheat seems odd. I can't see any physical signs of damage.
It is always connected to the PC via the USB In/out, both XLR outs to studio monitors, and the 1/4 out back to the PC via a Rocksmith cable during this time. Having only the power cable attached and letting the unit idle would reproduce, and unplugging everything except the AC cord does not allow the unit to start again any sooner.
I had tried 1, 5, 6, and 7 on this list and none of them had any effect: https://line6.com/support/page/kb/effects-controllers/helix/helixrackltfxstomp-reset-procedures-and-troubleshooting-tricks-r768/
EDIT: Support said to find a service centre and get the unit looked at, as it sounds like a hardware fault.
Yesterday, my unit seemingly fully died as per the original poster's and will no longer turn on at all. Changing the AC cord for a known good one doesn't make any difference.