Senators, especially committee chairmen, have quite a bit of implicit leverage, beyond the direct leverage of subpoenas or directly cutting funding to an offending agency.

Any given Senator is to some extent constantly in a favor-trading game with executive branch officials. People from the President on down need congressional cooperation to get their pet provisions into bills, programs funded, nominees approved, etc. A Senator can tell a White House official "I'd love to help you with that, however I have this issue with this agency not responding to my requests". Assuming it's a reasonable thing, whoever at the agency is in charge of this then gets an irate call from their boss's boss's boss ordering them to cooperate.

Of course this mostly doesn't actually get played out, because everyone understands the dynamic that defying senatorial requests will ultimately cost the President in terms of cooperation on other issues. So the norm is mostly to comply with reasonable requests, unless you're quite sure that it's a top-level priority where the White House really wants to take a stand.