When a cat goes out of remission, it can be harder to get him back there than the first time around. It can still be done, but you may find the journey isn't the same as the first time.
Many things can knock a cat out of remission: steroid shots, food change, infection, dental issues, etc. Has your kitty been checked to make sure he doesn't have an infection?
Here's a simplified explanation of bounce. When a cat's body is used to running on high sugar levels, the liver can freak out when those levels fall, even if they are still high or fall to normal levels. "Help," the liver shouts. "We're crashing! Release all the stored sugar!" The liver and pancreas release stored sugar, which can bump the sugar levels quite high. Take a look at my Billy's speadsheet at line 13. Textbook case of bounce. His BGL were starting to drop into normal ranges, and bam, one morning his BGL jumped up to over 400. You can also see what I did about it, which was absolutely nothing. It was so tempting to raise his insulin dose that morning, but you don't want to dose for the bounce. You want to change doses based on the lowest mid-cycle readings. Bounce usually clears itself up in a few cycles. (Forgive me if I over explain. I know this isn't your first rodeo. I'd rather say too much than too little.)
Now, I am not used to reading numbers on a pet meter, so you may want to wait for advice from someone who is. Looking at your chart, it doesn't especially look like bounce to me. A clear sign of bounce is when the nadir (lowest reading) is at least 50% lower than the pre-shot reading. You might consider raising his dose to .75 for 3 12-hour cycles and see how that goes. Monitor Moe and be ready to drop it back down if necessary. He had a nice low reading a few days ago. It's possible his pancreas just needs a tiny bit more help to keep healing.
Tagging
@Deb & Wink because she is more experienced than me and I'm not familiar with the specific insulin you are using.