If you are getting the error "Remote Invocation Failed, Due to Status Code" while searching records or downloading files, it is specifically because you do not get a status code back due to local network connectivity issues.

It is sporadic because it is probably tied to infrequent network issues at your end where the app can't make a call out to download the files from the Salesforce account to your browser/machine.

Try switching to another network and reloading the page.

As Options B, you may try lowering the number of files you are trying to download at once, say 200 at a time.  200 files seemed to be the sweet spot for customers who faced this issue.