I'm sure I've heard someone mention this before, but I've never seen it myself. Are you watching an unusually high amount of replays (let's say more than about 5-10 per day)? Does the limit go away the following day (may need to wait til after midnight site time, which is Paris time)?
I think this is the thread I remember seeing:
https://boardgamearena.com/forum/viewtopic.php?p=227414. It mentions two other threads, one of which suggests a limit of around 20-30 (as a guess), the other seems to suggest 80 (also as a bit of a guess). So I guess yes, normal, and my two questions above possibly apply (in other words, if you're not watching a high amount and your access doesn't return within 24 hours, then it's possibly a bug).