The 6 year limitation mentioned by Mr. Nitesh Ahuja applies to co-operative societies in Maharashtra only. Further the 6 year period is not for a legal heir to claim from the nominee. It is for the nominee to claim from the co-operative society.
As for the legal heir to claim from the nominee, I do not know whether there is any specific limitation at all. One will have to look into the respective law or into the law of limitation.
When a person dies, the person himself is not available to give directions with regard to his estate. The estate will go to legal successors under law if the person dies intestate and according to will if the person had executed a will. It is risky and bothersome for a bank, insurance company or other bodies to transfer the assets to a claimant. Succession laws can be complicated and it would be desirable to have the claim established by an authority like a court of law. Determining who is the rightful claimant is often risky even when a will is available. The will has to be genuine in the first place. Further even a genuine will can be disputed. In most States in India it is not enough to produce a will before a Bank or a Society. One will have to obtain a probate on the will from competent authority. A Society or a Bank would like to avoid all these difficulties. Hence the provision for nomination has been made.
Even the nominee being only a trustee is an escape route to avoid the problems of establishing claims. For all practical purposes, in default, a nominee is the rightful owner of the property. He can deal with the property as though he is the absolute owner until and unless a valid claim is made. A nominee is not an executor.
In the case of assets like cash it can disappear in no time once it comes into one's possession. A nominee can sell a flat, the next day it comes into his possession.
"Learn the laws of succession and be the wisest of them all." That was what Prophet Mohammad was reported to have said.