Your screen capture with "Object does not exist" refers to an Alias? Which would imply you already have a mapped object for it ... which doesn't work properly?
In which case, can you delete the current mapped object (which doesn't work - so no loss).
Then do a CTRL + SHIFT + A object spy (make sure you spy it, not map it - although I'm not sure it should make a difference) on it again. This should capture the properties at the point you map it. Even if it vanishes after that, you should still have the properties that were present when you spied it.
Don't try and drill down within any of the properties, that will probably cause it to lose/clear the object.
Do that, and then post the properties here.
I'm thinking you could .....
1. Simply put it in a double loop as soon as you activate whatever triggers it. One (very fast repeating) loop until it spots it. Then a second loop that waits for it to go.
2. Identify it by something simple such as classname (assuming there are no other elements in the DOM of the same class).
3. If using 1 &2, I would probably do all this dynamically and not map it.
4. If you *really* need to map it, your best bet is likely the caption (if it's text) or the image file name (if it's an image and the filename is exposed in the properties somewhere).
Without the element to look at ourselves, it's tricky to say.