Not really following you on this one.
You state that the Publisher machine is the one increasing in RAM?
But according to the png file, it´s the QlikView Server that gives the Error.
So first would be to identify, is it the QlikView Server that is the issue, or Publisher machine?
Second, do you have alot of qvws loaded on QlikView Server?
Any new qvws been added to the environment recently?
If so, test with removing the qvw and see if this helps.
Check with QlikView Developer/s if any new changes has been done to qvw file/s, as the issue just suddenly happened.
You can also check QlikView Server logs, and compare, Performance log with Audit log(needs to be enabled in QMC) to see when it happens and track if something specific is being "done". For example a selection etc.
Last but not least, you can use System Monitor to get a easy understanding of how the QlikView environment is.
Thank you for your valuable suggestions. After rebooting publisher server issue is resolved and now our Access Point URL is working fine. We will monitor for another couple of days, if issue re occurs I will use system monitor application to track down the qvw file which is causing the RAM consumption.