Well I have not yet had this issue, but I have done a ton of research (have a big binder from my research) and have a few general tips from other forums that I printed off for binder.
1) You may need to rerestrict his space. I am sure you would hate to have to cage him up in a pen (like a 4×4) but many people say its necessary if this happens to start over with litter training. Restrict his space, and he should catch on faster since he was litter trained earlier (i assume?). Either way this could be an issue of he just has too much space.
2) Change in environments for male rabbits especially could lead to this territorial behavior even post neuter. When you go to your boyfriend house, restrict the space, because he will likely be trying to claim territory the first few weeks. But have you recently moved his litter box? Changed his cage? Moved furniture around? All of this people say lead to bad litter habits.
3) Place his hay in the litter box, I use a hay rack to keep waste down, but most bunnies eat and poop simultaneously. This should ensure the BIG poops are in the box. Then you can start to delineate between marking territory and just regular pooping outside the box. But place hay IN the box not outside.
4) Buy a bigger box is a useful solution for many people. As the rabbits get older, they like space in their box. My box is like 3 times the size of my bunny but she is nearly perfect, she usually will turn around in it because she prefers poop in 2 corners and pee in 1 and hay in the rack. Small litter boxes=bad litter habits from what I have read in many bunnies. So look at getting a big litter box.
5) Medical issue. You could see a vet but I doubt this is the issue considering there is no other pee dribbles etc.
6. Is there pee near the litter box? Maybe you need a high sided litter box so that the butt doesnt hang over. Many people find this to be the case and the bunny pees over the edge of the box, which high sided boxes prevent.
Good luck hope these helped! But seriously, restrict his space and see if it eases up after a week or so. Sometimes its necessary. And expect territorial marking when you go to your boyfriends (expect it but hope it doesnt happen
).