Just keep changing up your workouts occasionally. You need to keep your body confused! Good luck
I daresay that's really not applicable in this case so much, apart from as the more I train the more i'm starting to question the truth of this statement besides...
Hmm. I sense some researching/an informed post on the horizon...
His statement might be correct when you look at your progress over the course of a few months and are looking to bulk up as fast as possible. Even for that matter it wouldn't be necessary to drop or change the routine every few workouts, but only after the gains slow down (can be 2 months or more). Then you can adjust volume, sets, reps, rest, etc, but that's a different matter!
The OP, however, wants to lose fat and gain strength so this is a completely different thing. Of course she might stall on certain exercises sooner or later, but this is not the time to switch to a split routine or something like that as her main goal is still to gain strength and not muscle mass (besides strength training also builds up some muscle mass, but less than a hypertrophy-based routine).
So in my opinion it would be her best bet to "reset" the routine or some of the lifts (starting strength and 5x5 usually have an easy resetting "mechanism") and just keep on doing what she's doing right now. If nothing helps she can still switch from one strength training routine to another!
I'd also like to note that it's a lot harder to gain strength when you're on a caloric deficit than losing fat and gaining muscle at the same time (because you can do both gradually). If the gains are too slow for you (while having reasonable expectations of course) you might consider eating a little more and staying just below your TDEE (maybe 200 calories below it).
