So, this should be fun.
I had "W3TC Compatibility Mode" enabled and used the shortcodes twice in a page. After caches cleared for that page, it would break on load after the first
echo (of any kind) in the custom page template being used—note that echoes in the header worked fine.
I disabled this mode and exempted the page from caching in W3 Total Cache's settings and things went back to working.