You can kick the bot from the game, skip the turn of the affected unit, and then reconnect it. Usually it doesn't happen on the next turn.
/who - to find out which player the bot is (should be 1 in a 1v1, but sometimes there are more bots)
/kick n (where n is the number of the bot)
/skip (or was it /skip n?)
Then there is a menu option to reconnect lost players. You'd also have to do that if you load a game.
Awesomes are awesome, but very slow, which makes them easy targets. Their PPCs don't to massive damage (30 damage if all 3 hit can be managed by some 3025 mediums), but they can reach out and touch someone pretty far away, unlike those mediums.
If an enemy is "crippled" it tries to get away (It is called forced retreat and can be turned off. In theorie you should do the same with your crippled units). The crippled state comes from different damages, if you hit it in the head with a ppc for example it would try to get away, because the head will now be destroyed if you hit it with pretty much anything but a single LRM.
Which hover did you have?
I just lost a 3058 Pegasus to consecutive motive crits. When it could only go 2/3 it got killed quickly. Because of the cold that would kill the crew within 1 turn I couldn't just abandon it either. It could have fled next turn.
I have infantry to rescue people as per against the bot rules, but 2 of the guys lost a limb, so they won't be going back on active duty anyway.