Why is my dog not eating food, has diarrhea, but still eats treats?

It is common for them to lose their appetite when they have a gastrointestinal disburance. Considering she has diarrhea, she is likely battling an infection, or food intolerance that is also making her feel nauseous. This may be due to another problem like a foreign body, or intestinal worms.

Diarrhea is a common problem and is usually self-limiting (will go away on its own). It doesn't appear to be serious right now, but it's always possible that it could be the start of something serious. If Abby has any of the following, then she should see a vet:

1) Blood in diarrhea
2) Very watery diarrhea
3) Starts acting very depressed
4) Stops eating (i.e. will not even eat treats) or drinking for longer than 24 hours.
5) Diarrhea lasts longer than three days.

You can often help them get through this by feeding bland food (boneless chicken and rice is good), but if she won't eat her normal food, then this may not work. Feed small portions (1/2 cup or less) three times a day. You can also add probiotics to the food (can get this at the pet store), which has demonstrated some efficacy for improving diarrhea. Ensure fresh, clean water is always available.

I hope this helps and Abby gets better soon.