@InvisionHQ, it is not about absence itself. It is about not talking with your clients. These are some suggestions :
Let your clients know, that you are on vacation and not available. Do it public, here in forum.
Create a kind of automatic reply that you send every time you get a PM. The same as above: "Sorry, I am on vacations."
Inform clients when you are available again, like "I'll be back on [date]". It is always easier to wait if you have a time frame.
React to the issues in your support topics, write anything, but write, do not ignore.
My personal negative example: I have posted a critical issue with your another app over a month ago. I have not got any answer, nor "yep, I will look into it [time frame]" neither "no, it might be critical for you, but I do not care" or just "I am on vacation now, be back [date], please do not disturb me". If you try change to point of view to mine, what would you think in this situation? By the way, I have uninstalled your other app, so no need to react any more.
Disabling apps - is not a good idea. Just tell your clients when you are available again and where they should report bugs. Here? On your site? A bug tracker would be helpful to see if there are unsolved issues and how many. Also to see how often you address the bugs. The issues in support topics are often overlooked.