In Battlefield 3 what can slowly damage my tanks?

This is a normal feature of the game: when your vehicle's health is below a certain amount (depending on the vehicle, and on server parameters), it is taking damage until it reaches 0%, or until it is repaired by an Engineer.

Source: my own experience, and this wikia page.

In Battlefield 3, vehicles that are reduced to a certain percentage of health will become disabled, having compromised movement and control. They also catch fire and will burn until reaching 0% health and exploding, unless repaired by an Engineer or by specializations such as an Extinguisher. The disabled vehicle must be fully repaired, otherwise it will soon catch fire again.

For most land vehicles, this threshold is at 50%, while air vehicles will not catch fire until ~30% health remaining.