I don't know what the reason that it suddenly started occurring for, but you can workaround it to get back to playing LSPDFR (I am not quite sure how to fix it to straight launch from desktop otherwise unfortunately).
Launch Steam and Launch GTA. Make sure that you select play story mode and NOT online.
Get past the loading screen (police chase, shootout, and any custom loading screens)
When you get the option to select story mode, online, and whatever else, alt+tab.
Launch RPH from your desktop. You may need to click it twice if it does not initially open. Wait for it to disappear to the bottom left of your screen.
Click play story and it should start loading your plugins.