The phrase "goes downhill" means that something deteriorates or gets worse over time. There are many synonyms that can be used in place of this phrase. Some examples include "declines," "suffers a setback," "takes a turn for the worse," "degenerates," "plummets," "slides," "recedes," "deteriorates," and "loses ground." Each of these synonyms offers a slightly different nuance, but the overall meaning is the same: that something is getting worse over time. These synonyms can be used to add variety to your writing or speech and to help you avoid overusing the same phrase multiple times within a piece of work.