So, I don't know much about this, but here's what I know and have cobbled together from experience and talking to others:

• The "no crosshair" glitch seems to occur only to non-host players.
• It can happen anytime during a mission. Often, you will begin a mission with crosshairs.
• It seems to happen when switching weapons. I haven't noticed my crosshair just disappear mid-firing, for instance.
• Perhaps most importantly: It seems to happen when you have Berserker equipped. I have done as many tests as possible and can reasonably confirm that the crosshair glitch doesn't require Berserker to have been activated, but rather that the perk is simply equipped.
• For some, it might suck to not be able to use Berserker, but given the usefulness of other perks and the rate at which my Berserker strikes miss/cancel, I don't think this is a bad trade-off at all.

TL;DR: If you're having crosshair problems, I feel bad for you son. I got 99 problems, but since I stopped using Berserker thankfully the crosshair glitch has not been one of them.