Keeping a TVS diode biased continuously?
In general, the 'rating' of a TVS is what's called its standoff voltage (\$V_R\$), or the voltage at which the device should never break down at. There's generally a leakage current (\$I_R\$) associated with this, which is very low (milliamps or microamps).

Once you go above this standoff point, the current will stay low but may gradually increase, until BANG - you hit the breakdown voltage, which is when the device actually 'fires' and clamps. Where this breakdown happens is a function of many variables; voltage rise time, temperature, etc.

As long as your battery voltage never exceeds the minimum breakdown voltage of the TVS, you're only dealing with leakage and not breakdown. The TVS will dissipate power but should not be harmed as long as the junction stays below its maximum temperature rating.