Julie,
What is your routine like in terms of E,A, and S? Can you post some of the times. If your A time is not long enough then your LO will be undertired, wake up at 45 mins and not go back to sleep as she has had enough sleep for the time she has been awake. So, that is a long way of saying ... maybe extend A time!
Callie is 3 months old too and is doing between 1hr 20 and 1 hr 30 A time, including Eat and wind down. All LO's are different of course, but that might give you an idea as it is a pretty standard A time for this age group.
If A time is good for her age then maybe you could try W2S? We never had much success extending naps with pat/shh once she was awake. Worked really well for DD1 but not this one! W2S has worked great for us, extending most naps to 1.5 hours now.
If all else fails and she is awake after 45 mins I usually just follow her cues and make the best of it! If I know she won't resettle I hold off feeds until regular feeding time, unless she is hungry otherwise she snacks and the whole cycle repeats. After feeds I go by her cues again and usually put her down as soon as there is a hint of sleepiness. I have tried to put her down say at the hour mark, but often she is not tired and then has another 45 min nap
, so I would go by her cues.
Does that make any sense!?