Two possibilities for the attempting to connect:
In ActiveSync on the Axim, check Tools, Options, Mobile Schedule (tab) and make sure the "When syncing wirelessly" options are each set to manual.
If you have an email account set to download at regular intervals, it will also try to connect. The solution I found was to select ActiveSync as the account from the Inbox account list when you are not actually connected.
When you say 'remember the partnership on both computers' - are you trying to sync wirelessly to two PCs? Do the PCs want to set up a new partnership each time? One possible solution is
IP Manager. This saves network settings and PC partnership names. You have to chose which PC you are connecting to prior to attempting to sync.