If Razorgrass Screen blocks during the first combat phase of a turn, does it need to block during the second one (created by Relentless Assault for example)?

I can't find anything specifically in the CR about it, so I'd imagine we're supposed to read it with the standard meanings of those terms. thus, if it's already blocked during that turn, it has fulfilled its obligation and doesn't need to block again.

There aren't many cards with such a blocking requirement, but it's well-established how the attacking version works, where there's a difference between each turn if able and each combat if able.

If the Screen has already blocked this turn, there's no requirement for it to block again.

the oracle text specifies "each combat if able"

That change was made with Ixalan. The question was asked and answered before its release.