Well...I had this issue come up a couple of times, but after syncing via USB and resolving all issues, remote syncing worked flawlessly.
Obviously you should make sure your conflict resolution settings in Activesync are not set to "Leave issue unresolved."
Also make sure your Axim is named something like PocketPC or AximX5 instead of Pocket_PC or Axim_X5. I know this makes a difference for network sharing (it doesn't like underscores..spaces..etc) , and this could also affect your Remote Activesync ability.
...if you've already done all of this, I would next suggest that you delete your partnership and create a new one.
be sure to check out
wifi.aximsite.com ...that site helped me resolve all kinds of strange wifi stuff....