I think you're sort of misinterpreting the postmodernist stance on truth in history - or at least looking at it from the wrong direction. While it's true that postmodernists oppose the notion that the historical truth can be known - the notion that historians know the events from the past as they happened and can basically reconstruct the past - and they generally oppose the notion of "truth" in itself, this doesn't mean that the point of studying/writing history is gone, nor that there is no form of "truth" to be found in the past.

I've written about this before, so to just quote myself:

Personally, I think a large part of this is due to how we define the purpose of historiography. The traditional view is that we must know the past to learn from it, as well as attaching value to the reconstruction of the past in itself. The problem here is that if we follow this reasoning, it's essential that the past is knowable. If we accept postmodernism's premise that the past is unknowable, the very reason why we study history is invalid. And this purpose is very much attached to the perceived value of studying history. Which we're all very sensitive about. I think - again, personally - that we can acknowledge the unknowable nature of the past, while still having value as a discipline. For me and many postmodernists, the purpose of studying history has more to do with the present than with the past. By studying (our construction of) the past, we're essentially studying humanity, the present and ourselves - which I think is a valuable enough purpose in itself. The upside of this purpose is that the question of historical truth and objectivity is now irrelevant, as even if the past is a narrative constructed by the historian, it can still provide us with interesting insights and lessons.

Postmodernist thinking in general pushes disciplines like history away from any self-delusions about being a science. History, in this interpretation, is more of an art. But of course, the purpose and the necessity of artists in our society isn't exactly universally accepted. But to me, at least, introspection on behalf of the individual and of the collective is definitely worthwhile and even necessary in any healthy society - and it's frankly more valuable and useful than a knowable and reconstructed past.

If you're interested in the subject, we had a Monday Methods on the subject of postmodernism and the future of history a few months a go. It has some other views on the subject as well, as PoMo philosophy is still cause for a lot of controversy amongst historians.

Lastly, don't despair. Historians should never worry about relevancy - the only thing they should worry about is job-prospects.