Hi caadmin,
Assuming you are using tomcat only and not IIS for web client access, and given the fact that the problem is resolved by recycling tomcat, then I would say that this leads us to believe that the underlying issue is that tomcat is hanging or crashing. My guess is hanging. We have a great document on how to work with CA Support to troubleshoot a crashing or hanging process. You can find it here: http://www.ca.com/us/support/ca-support-online/product-content/knowledgebase-articles/tec608335.aspx
Download the PDF and take a look at that. Basically what you need to do at the next occurrence is check in task manager if javaw.exe is running. There will usually be more than one javaw.exe process - but if you look in task manager at the pdm_tomcat_nxd processes, there should be the same number of javaw.exe processes as there are pdm_tomcat_nxd - if there is not, for example there are three pdm_tomcat_nxd processes running, but only two javaw.exe processes running, then we know that one javaw.exe is missing, which could mean that it crashed. If the number of pdm_tomcat_nxd processes and javaw.exe processes are equal, then most likely the javaw.exe for service desk is in a hung state. The document will explain how to troubleshoot a hanging process. You can follow the steps to manually generate a process dump on the hanging javaw.exe process. The trick is to figure out which javaw.exe is the one for Service Desk. If you look at the "command line" column in task manager, or using something like MS Process Explorer, you can see the command that started the process - you are looking for the one that is %NX_ROOT\Catalina_Base\ (not Catalina_Base_SA, or VIZ - those are for Support Automation and Visualizer). Once you have the dump file and the crash dump template filled out, open a case with CA Support and we will look into the problem to see what the process was doing at the time it failed. This usually leads us to root cause.
Now as a side note - I see you are using 12.7 - just for your information, 12.7 will no longer be supported as of December 31st this year. You should most definitely look into upgrading SDM to 14.1 at this point.
Thanks,
Jon I.