How recent should my bank statement be when applying for a Schengen visa?

You are applying for a short-term visa and you have determined that the most recent bank statements do not present your financial standing as favourably as older bank statements. You contemplate submitting just the older bank statements and now ask if that strategy has unacceptably high risk.

The technical name for that strategy is 'prevaricating'.

They do not like it and if they suspect that you are prevaricating your credibility will be damaged. Additionally you will get a refusal on reason #8 (or its equivalent) which is bad and matters will be worse because damaged credibility carries over from one application to the next. Financial standing, on the other hand, does not.

An alternative strategy is transparency. This is defined as an honest way of doing things that allows other people to know exactly what you are doing.

To use this alternative you would assemble the necessary documents without regard to how they make you look. If you think your recent bank statement paint a bad picture, you can use word crafting and composition skills to explain it away. To get started you can write something like...

My bank statements for May show that the balances are lower than previous months. This should be treated as an extraordinary variance because multiple one-off events occurred simultaneously. The most damaging event was blah blah blah; and secondarily the account was nearly depleted by blah blah blah. Note that all of these events were handled from my existing reserves without creating indebtedness. As mentioned previously these were one-off events with no likelihood of repeating; I expect the accounts to be fully restored to their normal state in July and blah blah blah blah.

It goes without saying that your explanation should be relentlessly honest. They love that sort of thing; they eat it up... especially if the English usage is polished and constrained to factual evidence (i.e., nobody wants to go through a long-winded, needlessly complex explanation). And oh! Avoid using my exact words!

There are no silver bullets in a short-term visa application; You can still get refused because your finances may not be that healthy. But the refusal reason will be you have not provided proof of sufficient means of subsistence... (or its equivalent) and your credibility will be intact. It means they will be more likely to believe you in future applications.

Prevarication versus transparency. Both strategies can lead to refusals, but only one assures that you don't get a credibility hit.