Just in case it helps someone else in the future. I was having problems with the Sage Pay Suite Pro from ebizmarts on a development site, it was hanging after pressing the “place order” button, and then taking over a minute, before moving to the success page with the payment taken.
First assumption was that it must be a conflict with another custom module, or the theme, and so I started disabling other modules and enabling as much logging as possible, without any joy. I then tried setting up another payment method (cash on delivery), and after pressing “place order” the success page loaded almost immediately.
I tried a different integration method (server rather than direct) but it was also very slow. It occurred to me, it might be the domain name (using a test one, rather than the one registered with ebizmarts). So I used the host file, and updated the development magento site to use the registered one. But no, still really slow.
A bit more googling and I came across this page. I disabled the profiler in the Sagepay settings, and the checkout time was back under 10 seconds. A bit strange because the same issue wasn’t present on the live site, but this seems to have resolved the problem.