It has been pointed out to me that some people having been having trouble booking tee times using an ipad. I then had the issue myself yet managed to book with no problem on my PC. On further investigation a day later I was able to repeat the problem.
I managed to resolve the issue instantly with a reboot of my ipad. This just involved closing it down properly (in my case holding the top button till it switched off), left it a few seconds and then booted it back up by again holding the top button till the "apple" appeared. Hey presto! I hope this does the trick.