This isn't a problem with Minehut, it's either a problem concerning the server cap or your server. Firstly, one reason that might be causing delays is the maximum server capacity of 3,450 that Minehut has in place, unfortunately, servers cannot start up beyond that amount (go to https://minehut.com/ and scroll down for live statistics, including this capacity).
The second reason that might be causing this is a corrupted server file that's delaying/stopping your server's startup sequence. What you have to do in this case is, most importantly, make a backup of your world by downloading it (guidance: https://www.youtube.com/watch?v=1DcfYlre6AA) then, go to the Danger Zone on your Minehut control panel and select select Repair Files. This should fix the issue, however, there is a chance that your world will reset after doing a repair, but as long as you have the downloaded world file, you should be able to upload it (guidance: https://www.youtube.com/watch?v=AeJ71A3-6pg)
To conclude, what you've described most likely is just to do with Minehut reaching the server capacity, and the best thing to do is just wait.