Servos don't generally get weak, they usually break off teeth and fail completely. I'd suspect your receiver pack is weak or needs recharging in the first truggy.
Your second car may have suffered the broken teeth symptom, but it sounds like you may simply have your steering or throttle reversed on the radio, causing it to center incorrectly when you turn it on. Between kids and transport the radio settings can easily get messed up.
You'd probably get better advice and response posting in the Nitro off-road forum.