How to configure Membership Status Rules so expired members can renew?
I think there are 2 separate issues here.  I'll try to tackle each.


  Using the plus [+] or minus [-] sign does not get retained when saved


I just tested on Civi 4.4, and a minus sign is saved, a plus sign is not.  An unsigned integer is considered positive here. If this isn't what you're seeing, try to replicate your situation on the demo site.


  Oops, it looks like there is no valid membership status corresponding to the membership start and end dates for this membership. 


CiviMember works by evaluating the membership status rules in order.  The rules may overlap - for instance, a "current" member can be start date to end date, and a "new" member can be start date to (start date + 1 month) - in that case, whichever rule comes first takes priority.  However, you can NOT have a gap where no status applies.  That's what causes this error.

Given your particulars, my guess is that your users are trying to create an "upcoming" membership - where the join/start dates are in the future.  Unless you create a membership status that covers that (e.g. "upcoming is (start date - 1 month) to start date"), you'll get this error.

If this doesn't answer your question, please edit it with concrete numbers - what your membership status rules are, and what the join, start and end dates are for a membership that causes this error.

UPDATE: I know this is months old - but I just saw your update.  The "Grace" period ends 12 months after the end date - but expired doesn't take effect until 13 months after the end date.  You'll see the error you're seeing for anyone whose membership ended between 12 and 13 months ago.  Set your "Expired" to take effect 12 months after the end date, to match the end of the Grace period.