It depends on the individual relationship and what flaws are coming up. I guess I got lucky in this process...at first my girlfriend was all about what I wanted to do and encouraged me to apply anywhere and everywhere. She didn't want her feelings to get in the way of my decisions. I later found out she was upset about the fact all my schools were so far. I then changed my list up a bit to compromise. The plan is that if I go away for school that she will join me asap (probably within a yr) even though she has an established position at her job. We have been together 5 and a half yrs at this point and have done long distance about half of our relationship. I think that the grad school process puts a strain on anyone's relationship no matter how strong because big life choices are looming.
As far as going it alone- I personally need my girlfriends support. She already went through grad school and I supported her and now I need her to be there for me. Of course though if your relationship would end up distracting you from your studies then its not worth it.