A position without a reason is fundamentally a premise, where the premise is simply much more profound than usual. Since every non-trivial argument is based on a subjectively procured premise, it follows that the validity of every argument hinges on the validity of a premise.
For example, take the axioms of mathematics. They are premises. The mathematics (the part which is not intuitive but hinges on the validity of the axioms, like, say, Banach-Tarski) hinges on the axioms. Hence, validity of the result hinges not only on the strength of the argument, but also on the validity of the axioms.
So, given that, any position, whether it is an argument from a premise (i.e., a position "with a reason"), or simply a premise itself (i.e., a position "without a reason"), is equally valid, since it hinges equally on the validity of some premise. Or, rather, perhaps they are not equally valid, since the position with a reason also hinges on the strength of the argument. This is an extra source of possible weakness. Hence, the position without a reason seems to be at least as valid as the position with a reason.
So why is it often believed that any position without a 'reason' is invalid?
I believe this statement should be modified into something like
Given all the premises which a group of people all take for given, then, within that group, any position without reason which is not identically equal to one of the given premises, is invalid.
This is of course an entirely different statement than the more general "every position without reason is invalid" since that applies across all groups and across all premises. I seem to have shown this statement to be identically idiotic.