I'm not familiar with Indian law. However, as a general principle which should apply in most, if not all, jurisdictions, limitation periods apply to date by which you must bring your case to court. They do not relate to evidence.
With that said, courts attach weight to evidence. Depending on the context, older evidence may be given more or less weight. For example, witness testimony based on events from years ago may be seen as less credible as it relies on memory. On the other hand, written evidence which is contemporaneous (from the same time as the facts it evidences) may be more valuable than more recent evidence for the same reason - it is more likely to be accurate.
"A might be using delatory tactics so that the evidence gets old and he can take his venegeance"
Rules of court may punish such behaviour. For example, in england-and-wales, paragraph 4 of the practice direction for pre-action conduct states:
A pre-action protocol or this Practice Direction must not be used by a
party as a tactical device to secure an unfair advantage over another
party. Only reasonable and proportionate steps should be taken by the
parties to identify, narrow and resolve the legal, factual or expert
Breaching such a rule shouldn't affect the outcome of your case, but it can have cost implications.