I set up a new event which was a copy of a previous event in early Feb 2016. The front end component accepted registrations up to 21 March 2016 and since then has stopped doing so.
I have tried setting up a new copy of the event but this made no difference.
I have also upgraded to latest version of DT Register but this also made no difference.
As this site is running in Joomla 1.5.26 I am pretty sure nothing else has changed in that period to cause it to suddenly stop working.