To answer your question OP, that's never happened to me so I don't think it's normal. When I switch my buildings to trader mode, the little trader ships start moving again. Don't know why yours stopped, but it seems like there are a handful of random bugs out there. You can try sending in a savegame and maybe the devs can iron it out.
the "longest trade route isn't really the longest" is another problem. Don't know how that's supposed to be calculated... but it often gets borked. and it's not clear what planetary bodies will break the line. I've had dead uncolonizable astroids break my trade line, frustratingly...