I was testing Offers last night for one of our groups, and I was able to get the Offer to return.
For testing, I created a Fixlet to create a Testing.txt file in a folder. The Fixlet was relevant if a Windows computer had the folder without the file.
I deployed the Action as an Offer, configured to re-apply if it ever became relevant again.
When I accept the offer, the file is created. If I then deleted the file, the Offer returned in a few moments.
You might need to adjust the Relevance so that once the log file has been accessed, the Task becomes Relevant again. Without knowing how your relevance is written, I’m guessing the Task never changes It’s Relevance State when you accept the Offer, so the client never sees it “become Relevant” again.