Every time I search with some filter (under the regular tools option or advanced search), the filters disappear once I search another term. Is there a way to make the settings stick somehow?
I don't know of a dedicated option to make the settings stick, but a workaround is to change the URL instead of the search field.
Suppose you're searching for images of red flowers:
The search term, 'flower', appears both in the search field and in the address bar. If you change it in the address bar to e.g. 'shoes', Google will remember the settings because they're in the other parameters in the URL: