If there is nothing specifically wrong with my church, but I feel like I've stopped growing, is that a good enough reason to look for another one?
I doubt it. I'm taking seriously the statement, "there is nothing specifically wrong with my church." There is always something wrong with your church!
So I'm just assuming this is a doctrinally sound church and a church in which pastoral care and mutual love is happening, and so on. And I would say, if you've stopped growing then you can't point to your church. It sounds like you can't blame your church.
Something else is going on here, and you need to dig down to the obstacles that emerge in you, and find out whether it's because you've stopped serving or praying or giving your life away. Given this first statement, "If there is nothing specifically wrong with my church, but I feel like I've stopped growing," I would say, do not assume going to a new church is going to change that.
What will happen in a new church, probably, is some artificial new buzz. The worship will sound different, the preaching will sound different, and the difference will feel energizing for a while. But it's artificial. It's probably not the main cause, and you're going to bump into the same stall at that church.
And if you keep doing that, you're going to fail to find out what the problem is. Because I think the Lord would have us grow continually in a church as long as we're there and as long as life lasts. And growth has lots of other obstacles to it than church.
So get people around you who can counsel you as to what the real issue is here, why you're stalling. And it probably isn't church.