Thank you!
I have tested as much as I could, but everything worked normally – even if I tried uploading bigger PDF files, like over 50MB. My guess is, that the server may be reaching some performance limits, and throttling at some point.
To make sure the search works as optimially as possible, I strongly recommend using the index table engine on all of your search bars. It has huge performance benefits – and it may as well resolve these issues as well.