Just to be clear, I muddled the two together before...
1) Stopping halfway, more likely to be a security feature as the AP realises it is coming under attack, -t option to initiate timeouts to make attack less obvious. Consider using -d to delay between pin attempts for the same reason or if the AP security periodically locks out WPS pin attempts, set the option -l (time in seconds).
2)Not starting, WPS not enabled, stopping Reaver from being able to work full stop.
Like jroy08 said, stopping and starting helps, but it is possibly an issue with inbuilt AP timeouts, try the above commands. I have never had Reaver fail once I worked out each routers quirks, even with those directly next to my interface, possibly again, idiosyncrasies in different router types.
Just keep experimenting with different AP's/conditions/settings.