So far lost a 16, 17 and T1 due to falling through the Earth and similar weirdness. A T7 the other day to the Kataris26 ambush (3 rocket choppers at the door, after cut scene). Have a T34 currently up and running, only have to get the T1 (Gold) skin, because it didn't unlock the first time.
I don't actually have a problem with Choppers and bikes. It's bounding from choppers you have to be careful about. I'd recommend not doing so til the chopper is stationary, once landed. -- For some reason, choppers hitting the the ground seem to temporarily (split-second) drop you below ground level and if you bound at that point (whether due to an emergency or otherwise) you can continue to fall. -- If you look at a stationary chopper, you'll notice the wheels sit below ground level. They're not actually flat (as they should be). Perhaps that has something to do with it?
Other than that, things get very strange once in the high tiers (20-1). Whether it's actually on or off doesn't seem to matter. Just watch out for that.
When using bikes: wheels up to mantle/jump; point down when landing. Mis-time either and you can go flying for 100m or more!.. without the bike.
Don't actually brake with bikes. Pepper the throttle when hard cornering instead. -- They are different from the 4-wheel vehicles, you generally use the handbrake with.