One workaround I found is to equip the gear, then close and restart the app. After restarting, the gear remains equipped and will appear correctly on your profile.
Are you still seeing the issue? I just tried to reproduce with my avatar + gear that I own and I was able to successfully save an avatar / outfit containing that gear. Swapping between avatars showed that the gear was successfully saved to my avatar.
As the OP, I’m happy to confirm that I’m no longer experiencing this issue! However, I’ve PM’ed you about another issue that’s similar. If needed, I can file a bug report for that separate issue (just let me know). Thanks!
I just wanted to follow up here to say that bug reporting staff have manually approved the report and converted the PM. Also, I’ll mark your post as solution. However, if anyone is still experiencing this issue, please let me know, and I’ll unmark it. Thanks!