I know it is preferred to go from a lower gravity to a higher gravity when reusing yeast.
But would going from a 1.060 to a 1.045, really be that bad?
It just isn’t going from low to high. It’s going from an environment that produces yeast (vs. produces beer) so that you have healthy yeast to reproduce. That said, don’t do it. 
On the other hand, go for it!!! 1.060 is not that high and as long as you haven’t been pitching batch to batch for a long time you should be fine, (read that as I frequently do it)
Where “High Gravity” begins is debatable, but for the most part, anything less than 1.080 to 1.090 can be re-pitched with no issues, either higher or lower. Much above that, what happens is the yeasts “mutate” that is they change the way they work. The changes allow the yeast to process the higher gravity/higher alcahol enviornment better without dying. Once the yeast mutate for the higher enviornment, they do not change back to “lower gravity processing mode” very easily.
Re-Pitch with no reservations!
Yeah, 1.060 isn’t that high, you can generally repitch from there with no problems. If the beer was really hoppy though, you might want to make a starter or wash the yeast a couple of times to help remove some of the hop residue from the yeast cake.
I like the “make a starter” idea. Fresh, active, healthy yeast is a viable option. That being said, you should be fine repitching as long as it’s within the window of opportunity.
Even if the yeast has been used for high gravity say 1.090. If you have a huge biomass of about 2 quarts and it hasn’t sat around for more than 3 or four weeks, I’d say there’s enough viable yeast left to do the job at a gravity of 60 or below… I have done this many times with good results. If you are worried then use some to step up in a new starter like Bluesman and others have stated…