I'm not sure what causes this problem seems to have something to do with 64bit O/S or office 64bit, I've seen it in 2010 as well. I tried running different custom functions to alter the database options via vba, all with limited success.
I ended up creating an AutoExec macro that runs the equivalent to DoCmd.RunCommand (acCmdRefreshSharePointList)
go to Create tab > then select Macro under 'Macros & Code'>
then add the 'RunMenuCommand' action,
and set the 'command to run' to 'RefreshSharepointList'.
and upon saving the macro, ensure it is called "AutoExec" and nothing else.
Let me know if this worked for you.
Update:
I've been getting occasional errors when using the above method, if it works for you, great, if not, try this.
insert the following function into a module, replace "table1" with any linked sharepoint table in your db:
Function refreshList()
CurrentDb.TableDefs("table1").RefreshLink
End Function
Using the same procedure as above, insert the 'RunCode' macro step instead of the 'RunMenuCommand' and in the space enter 'refreshList()', this should invoke the login prompt correctly. Note: just remember to make sure you don't have a form that uses sharepoint data opening up when the database opens by default.