how many times I can reuse the tapes??
There is no hard and fast rule. It depends on how often the tapes are used, storage conditions, the state of your tape heads, etc. I know some installations replace their tapes once a year. LTO tapes have a built-in microchip which stores some statistics. I have seen an expensive device which reads these statistics and give you a score as to how reliable the tape is.
When it comes to replacing tapes, just remind the bean counters how much is the failure to recover from a disaster going to cost the company. It is no good having a backup which cannot be restored because the tape is unreadable.