This in my understanding of the text ... I haven't worded it the best, but I hope it helps. "I was slipping" is being used figuratively or symbolically here. The speaker is trying to escape or move on from some past problem in his life related to Julie Baker. But he slips or stumbles in his attempt to move on (by looking at the paper under his pillow) and he struggles to escape this memory of her. The speaker is trying to forget Julie Baker, but we are not told why in the text. Perhaps a broken romance and he is trying to forget and move on with his life, or perhaps there is some other reason. But the speaker is telling us he has 'stumbled' or slipped in his attempt to move on or forget her. He had slipped/stumbled in trying to forget Juli Baker by looking at the paper under his pillow. I assume this paper is connected to her in some way. "I was slipping" ie. I tried to forget her, I tried to move on but I have failed (temporarily) in this by reading this paper connected to her. I have slipped .... I have gone back and thought about her again to perhaps let her in my life again.

“Slipping” is often used to describe the situation of losing one’s resolve. His New Year’s resolution was to lose weight by not snacking. But he’s slipping. He had popcorn during the movie yesterday. This is probably the sense of your example. You can also use “slip” to describe an unintentional transition to a mental or psychological state. He’s gradually slipping into a state of depression. According to the nurse, the patient has been slipping in and out of consciousness.

Hi markhu26, thank you for your question. The world 'slipping' in the current context means sliding into a sleep as the result of exhaustion. Here are some universal definitions of the word. verb 1. lose one's footing and slide unintentionally for a short distance. "I slipped over on the ice" 2. go or move quietly or quickly, without attracting notice. noun 1. an act of sliding unintentionally for a short distance. "a single slip could send them plummeting down the mountainside" 2. a fall to a lower level or standard. "a continued slip in house prices" Keep it up.)

No native here, but I think I've got a good understanding of the word here. So when you're "slipping" you lose your balance and probably fall, as in you lose control. Same thing here, really. It's just that that slipping is figurative.