What technical problems stopped scramjets from being used on hypersonic aircraft?
I'm don't research hypersonic flight, but I bet the primary barriers of hypersonic flight are less technological and more political/economical. After all, we pay money and conduct research in order to solve technological problems.

You would think that developing an engine is primarily a task for aerodynamicists since they can design better intakes, compressors, nozzles, etc. However, materials science will typically limit what an engine manufacturer can actually build as you mentioned in your question. Let's imagine aerodynamicists design can design a scramjet that can reliably run for a thousand cycles, but the engine is useless if the aircraft's skin can't handle the high speeds. 

More importantly, who's willing to pay for super-inefficient scramjets? Commercial airliners (consumers) weren't even willing to pay for the supersonic Concorde, so you can easily discount them from buying scramjet-powered aircraft. That leaves the military. In the 60s, the military was willing to pay for speed (see SR-71, XB-70), but then stealth became more attractive than speed and super/hyper-sonic research fell by the wayside.

Now the US, China, and Russia are again funding hypersonics research in part because stealth is losing its advantage. Moreover, some startups (Aerion?) are exploring supersonic business jets for the really rich folks, so you're starting to see their engineers exploring hitherto exotic supersonic tech. However, hypersonic flight will still be beyond the means of an average consumer.

TL;DR: Hypersonic research probably stopped less because of tech problems and more because stealth offered more bang for the military's buck. Now the pendulum is swinging the other way. Military supersonic technology is also making its way into the commercial sector for the uber rich.