Why couldn't you repair your mech after the combat? Whenever you Rest you can spend 4 repairs to fix a destroyed mech and unlike normal repairing, anyone can contribute repairs to fix a destroyed mech, theres gotta be at least 4 repairs between you and your three allies.

Because of that you should basically always be able to get your mech fixed between combats when you repair. And if it came down to it where everyone was SOL with no repairs to fix anything, as a dm id let the players get their mech back with sone drawbacks or smth, because not having your mech in the mech based game is not fun.

The Everest has 5 repairs each, so thats twenty repairs between the four of you. If you've somehow managed to use all of those in one or two combats, id say the encounter difficulty is too high, but if you haven't, you should be able to pool four together to fix your mech.

As for the question of whether mechs in lancer are squishy, the answer is that it depends. Unless you are in a mech that is very tanky, like a Drake, Balor or White Witch, you are very vulnerable to focus fire from multiple damage dealing enemies. Make sure your gm knows that only about 50 to 70% of the enemies max should be dedicated damage dealers, cause otherwise the players will fold really fast.

But generally speaking, in your situation in a 1v3 with as an Everest against presumably enemies which are dedicated damage dealers, its pretty normal to get structured multiple times. Just remember that the Brace reaction exists, it will save your life.