There is almost certainly a PHP limit being reached when Showkase tries to process your large gallery.
Each image has a number of different variables attached to it and a certain limit might be exceeded when your gallery reaches a certain number of images.
First of all, try increasing the max_input_vars PHP directive on your web server. (Please see here for details).
The max_input_vars PHP directive might be set to 1000 so try increasing it to something higher like 5000 instead.
Your web host should be able to help you out with this.
If the value of max_input_vars is not the problem, then the memory_limit PHP directive is the next most likely candidate.
The default value for the memory_limit directive in the current version of PHP is 128M (as noted here) so if yours is lower than this, I would recommend increasing it to 128M to see if this helps.
Hopefully increasing max_input_vars and/or memory_limit will solve your problem.
Also, please ensure that you are using the latest version of Showkase (v1.4.1).
Version 1.3.4 introduced "More efficient use of server memory allows more galleries in one web site.". (Please see the Version History for a list of changes between versions.)
If necessary, instructions for upgrading Showkase can be found here.