In T184948 a work around was applied that added a rate limit even to bot accounts that were previously without a rate limit (https://gerrit.wikimedia.org/r/#/c/427156/). On the task we already complained that this is not the right solution and it looks like mass message is broken because of this, see https://www.wikidata.org/w/index.php?title=Special:Log/massmessage&dir=prev&offset=20180420005019&limit=100&type=massmessage&user= for a snippet
This seems inherently broken, the noratelimit right exists for a reason. I'm not really sure how to work around this in MassMessage besides disabling rate limits I suppose?
Did I miss an announcement to wikitech-l/wikidata-tech that something like this was going to happen?