Properly basic beliefs are those beliefs that are justified without reducing them to any simpler axioms. Examples of properly basic beliefs are: a) that minds other than my own exist; b) that there is an external world; c) that the past is real and we have not been spontaneously created five minutes ago with false memories of a much longer past. I could go on, but I think it suffices to say that we have more than enough properly basic beliefs. We don't need to argue that these beliefs are true. Instead, we are justified in believing they're true simply based on our immediate perception of their verisimilitude.
I suggest that the Principle of Sufficient Reason (PSR) is a properly basic belief. Sure, there are plenty of arguments in support of the PSR, but suppose all of these arguments are unsuccessful. Even under such an unlikely scenario, I suggest we are no less justified in affirming the PSR.
1. Intuitively-held beliefs are justified barring any defeater. (Premise)
2. The PSR is an intuitively-held belief. (Premise)
3. Therefore, belief in the PSR is justified barring any defeater. (From 1 and 2)
If the argument is correct, then the burden of proof is no longer on the theist to demonstrate the rationality of belief in the PSR. Instead, the burden of proof has been shifted to those skeptical of the PSR, and those who maintain that belief in the PSR is not only false, but positively irrational to believe in. That's a tall order to fill.