I don't mean this to be harsh/negative in any way, but when I read your posts (esp. your initial one), I get the following impressions:
- you feel neglected by your g/f even though you talk every day and you know she's short on time/energy/sleep
- you're very concerned the relationship will fall apart even though you talk every day
- you want to be with her on a regular/frequent basis, though this isn't likely to happen until you head over in September
Never having met you or your g/f, I can only speculate, but in her position, I would feel the following:
- that I was giving more than I should to the relationship by talking every day and being short on sleep/high on stress (unless talking every day doesn't cut into her sleep time)
- that the relationship could fall apart if you're demanding more time than that and I'm not sleeping as it is
- that LDRs have to be dealt with and, by their very nature, mean you can't be together on a regular basis (you'd mentioned her wanting to go out of town with family rather than see you, which stinks for you but doesn't seem completely unreasonable)
Given all that, I echo what mirrajay and rynn have said...find ways to stay busy, try not to give off too many "needy" vibes (as that stresses people out at best, and turns them off at worst), and don't give her any grief/guilt trips about studying/wanting to vacation with family/etc. (I'm not saying that you would, but it's something to guard against, because having done the LDR thing myself, that also kills a relationship pretty quickly.)
Good luck...September isn't that far away, so if you can make it until then, things should be easier.