There is no time limit on how long Time Machine backups are kept, but there is a limit to the capacity of the drive on which they are stored. Once the drive fills up Time Machine will automatically start dropping the oldest un-accessed files off the back end of the data set to make room for the new files being added to the front end. The user is notified when this is imminent. So the Time Machine backup can be thought of as a moving window through time and the length of time encapsulated in that window is a function of the capacity of the Time Machine drive, the size of the data set that is being backed up, and the rate of change taking place within the backed up data set.
I don't know what the odds are that I could successfully recover a specific file from a damaged Time Machine data set. It could range anywhere from 0 to 100% depending on what caused the damage, where the damage occurred in the data set, and the extent of the damage. Even if the file is found in a damaged data set it could be incomplete or otherwise corrupted and therefore useless or worse (I have seen that happen but it not from in a Time Machine backup). To ME the issue is whether or not I could/would trust the data and MY trust level would be low, very low. Your confidence and trust level may be — apparently are — different from mine and therefore we are likely to make different choices.
