Interesting question.  There is generally no time limit on legitimate charitable restrictions, but since the foundation hasn’t specified the restrictions, this rule may not apply.  Without researching this question, I don’t recall ever seeing a case in which it was raised.

I think you are doing the prudent thing in trying to work with the foundation to understand how they would like the money to be used. I am sure you would like to be able to ask them for more at a later date.  But if they don’t respond to your latest request, I think I would send another letter (by a method that provides a clear receipt) saying that if you don’t hear within 90 (or some other reasonable number of) days, you will use it for general operations or for some specific purpose where you can spend it all productively. I would talk first with the state attorney general and copy that office on the letter. If the first letter doesn’t work, and you want to be particularly careful, you could try a second one.

Assuming you are in a state that has adopted the Uniform Prudent Management of Institutional Fund Act (which is every state except Pennsylvania), there is a specific procedure available to obtain court approval to modify restrictions if they become impracticable or wasteful. (See Ready Reference Page: “New UPMIFA Sets Rules for Management of Charitable Funds”) I think a court would be impressed with the argument that this lack of specificity is wasteful and would not think it reflects well on the foundation.

Depending on the size of the grant, you may decide not to bother to go to court, particularly if the AG does not require it and if you have enough reserves to cover the grant if the foundation ever comes back and says you spent it improperly. But it is hard to believe that it is likely to come to litigation if you give them a deadline and politely indicate the possible consequences.