I had the same problem, I was using Access 2010 (front end) which was linked to SharePoint 2010 List (back end). Everything worked fine until one day when the IT dudes updated us to Access 2013 which now doesn't want to connect to our SharePoint 2010 List. I was able to find one work around by selecting the "Golden Square" (link-to-list in the table column) right click > and select Refresh List. I only have to do that once, but I have to do it each time I open the db.
I found this code that solved my connection problems.
Public Sub updateData()
Note: (replace "linked_table" name with your actual table name and keep the quotations)... This worked for me...
I put the code in my Switch-Board (Form) so it refreshes "on load"... Switch Board > Design View > Properties > Event Tab > On Load > Code Builder > Copy n Paste vba string above > Save > Quit Access and relunch.
Good luck and let us know if this works for you.