Hello again

Did you manage to increase the A times yet? I think a couple of weeks back you were on an A time of around 1hr or 1hr 30 mins and were going to increase to 2hrs. Could you post your current EAS times please so we can see what's happening, jot down the real times, A is all time spent awake, S is from eyes shut and asleep to eyes open and awake.
PUPD is a last resort method. it isn't something that "works" in the sense that it puts your baby to sleep. Rather it is a method of reassuring your baby that she is not alone whilst she learns to go to sleep and to nap longer, so that she has your support rather than being left alone. It isn't a method we usually advise for 4 months and at any age we would first look at routine and other sleep training methods before resorting to a proper PUPD.
45 min naps indicate either than she is not tired enough or has not learned to self settle (independent sleep) or not learned to transition from one sleep cycle to the next. You can alter her A time to get to a suitable length and you can teach her to transition from one cycle to the next. W2S (wake to sleep) is often a great way to do this, it reassures and soothes baby before she fully wakes so she is still sleepy and teaches her the habit of sleeping longer. Have you ever tried it?
https://babywhispererforums.com/index.php?topic=223809.0If you look at naps option 1 it explains how to do a W2S. You can expect to go in 10 min before she wakes (so at 35 min if nap is usually 45 min) and to stay for at least 20 mins beyond the transition into the next sleep cycle, this could be around 30 min in all. If she takes longer to settle though you'd keep trying until the end of nap time, picking up if needed but otherwise soothing in the cot.
You might also need to do some sleep training if she is used to falling to sleep in arms so that it is not a surprise to her to wake up in a different place.
Also, many LOs take short naps at 4 months, it is a known developmental phase and even LOs who were previously sleeping independently and on a good routine can have troubles at this age. My own DS had 40 min naps 5 times per day for a couple of months during this phase and he had been sleeping independently since around 8-10 wks old. he returned to independent sleeping when the phase passed. it is often 4-6 months but can be earlier or later. My DS had his at 3.5 - 5.5 months.
You can continue to post to this thread with updates and we can continue to support you here as you find your way through this.