"Error during serialization" when modifying plot created from custom classes

I have been running into the following error in a couple of different situations:

Error using scribeccp. (Line 24)

Error during serialization.

The rest of the details vary depending on the situation, but it always occurs when I am trying to interact with a plot somehow. The two main instances are if I am trying to delete or copy a plot object. This happens whether I use the keyboard or the right-click menu.

This issue is almost certainly tied to the fact that these plots were created from custom objects functions. I have a number of custom classes with their own plot functions which I used to create these plots. I also store some of these objects in the UserData for the plot objects so that I can access them later.

What is causing this serialization error? Is there some function that needs to be defined for my custom classes so that it can be called during serialization (maybe a delete or copy)?

Edit: I dug a little deeper and tried running the command in scribeccp in debug mode so that it wouldn't go through the try/catch statement. Here's the command, and the error output I got back.

scribeccpHGUsingMATLABClasses(varargin(:));

Error using getByteStreamFromArray

Error during serialization

Error in getCopyStructure (line 10)

Error in scribeccpHGUsingMATLABClasses>ccpCopy (line 266)

Error in scribeccpHGUsingMATLABClasses (line 78)