I don’t know if it effects all modes, I play ARB only.

When you follow this to report a player after a battle, you have to wait more than half an hour to get access to the replay.
Is this a problem with the game or the website?
I don’t know when this problem began, I notice it for weeks now.
Nobody waits half an hour to report a player, and most players forget about it, if they continue playing.
The Server replay becomes available shortly after the match finishes. If you leave the match early then the server replay isn’t there because the match is still happening. Once the match finishes you can go to “messages” (envelope icon bottom right in hangar) and find the post battle information for the match, a link to the server replay is at the top.
As Necronomica said, replays are available shortly after battle ends.
If you cannot find your replay, please wait few minutes and check again.
Cheers!