I think I could localized the reason for your problem.
1. This Joomla installation seems not to be maintained really well.
2. It exists a lot of problems and it was not possible for me that it works with PHP 7.x.
3. After I had checked and tested a lot I took a look at the database. And here is the problem!
In the jDownloads system plugin was never typed in a limit value for the maximum amounts of logs. So it exist here in the meantime more as a million data sets
!!! When you now consider that by every download this table must be changed so It's no wonder that you see a longer break.
Please make this:
- open the jDownloads system plugin and type in a limit value for the logs. When you have assigned download limitations for user groups in jDownloads you should use a higher value (maybe 20,000 - 50,000). Otherwise should be a few thousand enough.
- save the plugin and wait now
until the page is loaded complete again! In the background is removed a million data sets and that needs time (maybe a few minutes).
- try now again to download a file and check the result.
I think that your issue should solved now (I could not really test it here).
P.S. I will add a default limit value in the coming new version 3.9 to prevent this problem in the future. Thanks.