I've had almost the opposite experience. VPN sort of worked, but I could not open a single HTTPS connection. The VPN problems I had I could trace to a bad WiFi connection (I had to lower my MTU and it worked fine).

Now, on previous trips I experienced what you mentioned. It seemed really like there was some machine learning going on, and after using a VPN for a while the connection would get bad. But I guess it might not be machine learning, there might just be a huge number of humans watching your traffic - which would explain why it is so inconsistent.

The thing that worked best for me is just using ssh -D (on most days). Our workplace uses ssh a lot for secure communication with outside china, so that couldn't possibly be blocked without hindering our work (and I believe 'they' have no interest in that). So whenever I had to access something for work that was sillily blocked (argh gmail), I just used the ssh connection that was open anyway.