Is there a time frame/limit for investigations?

[i am god]

My detectives haven't found any new frames for their investigations in several days, but I can't seem to complete the sequence. I failed an investigation because I took too long to arrest the culprit, is it possible to take too long to discover them and make the trail go cold?
Or am I just unlucky and would need to put more detectives on the case?

[Cometf]

If I remember correctly, the only time limit is 4 days for the actual arrest. If you're not getting new frames, you either have all of them and haven't found the right sequence or you need to have more/better detectives working on it.

Only the detectives in the current shift are working on the case that day, so that might also be factoring to the overall efficiency on any given day. But you really should have at least one detective from different shifts always working on a case, as the only other way to fail an investigation is if all the detectives on it die.

[Nikocadalus Avacadoela]

I don't remember having a limit, but some cases can get your detectives killed.