I have seen this too on an Xperia X. In my case what I found was that when I had one SIM that uses Three’s network and another one that uses EE’s, the SIM using Three had to be selected for mobile internet for it to work at all, otherwise I saw exactly what you describe. When both SIMs used EE, or one used EE and the other O2, there was no problem.
Three publish this support article that claims it is connected with the fact that they don’t use 2G. I have no idea whether it is true or not that the X or XA2 cannot support 3G or 4G simultaneously on both SIMs, but in the end I had to transfer the number to a different provider to get the full flexibility of the dual SIM phone. Maybe more recent models are better, but I’m not about to buy one to find out