Without knowing the web sites, it is difficult to guess what's going on but it might be a combination of the site's session management and rotating exit relays.
Tor clients rotate their exit relays regularly which means that HTTP requests to the web site will come from different IP addresses. Depending on how the web site implements its session management, it might get confused and redirect you to the main page to start all over. If the web site requires you to log in, you might even have witnessed cases where the web site logged you out. Given today's IP address mobility, it is not uncommon to send subsequent HTTP request from different IP addresses. As a result, that kind of session management can be considered problematic.
TrackHostExits option allows you to specify domains for which Tor will reuse the same exit relay. You can read more about it in the man page:
man torrc | less -p TrackHostExits. Also note that by using this option, you are trading off some anonymity. But then again, if the site requires you to log in, you will be pseudonymous towards the web site at best.