Hi,
Yes, I think you are correct here, it is very likely the limit and probably the incorrect ordering as well, as I checked the source now.
Well, if you cannot add access, I can only guess, but here is a solution you can try via overriding one of the files:
1. Make sure to have back-up first
2. Open up the wp-content/plugins/ajax-search-pro/backend/settings/class/wd_cf_search_callback.class.php file on your server
3. Replace it’s contents with this
4. Save, and reload the search options
If all goes well, typing in the “city” should give you the “city” custom field first.