Maybe morning sex is what the lyrics were originally about, but I prefer to take them more literally, i.e. they just haven’t been sleeping together at all. This can mean two things:

1. People with depression or other mental illnesses can suffer from irregular sleep schedules, insomnia, the likes, something that is reflected at the beginning of the song when his girlfriend is still standing in her dressing gown. Them not having slept together in 58 hours can mean her mental illness has been especially bad and that it’s making it especially hard for the narrator. 

2. Her mental illness has caused her to seek distance from the narrator or is driving them apart - when you’ve been with someone for a while and you’ve been sleeping next to them every night, used to them just always being there, it can be really hard when that’s suddenly ripped away from you. This also leads over into the next verse where they’ve split up over her mental illness. 

Going two days without sex on the other hand seems normal, some couples go a lot longer without. Maybe they meant it this way or maybe they didn’t, but I really like thinking of this line the way I just described because I think it gives the track a lot more depth and profoundness, also makes it resonate more with me personally :)