When you can't seem to figure out how to get your projects and ideas to sound just the way you want it to be.
Are you sure that actually is "technical constraints" that are limiting your creativity? I might be completely wrong but that sounds like someone not owning a problem "its not me! Its the gear, or lack of" - what gear are you referring to?
I usually find that technical constraints push me to be more creative, not less.
How much time have you really spent on it? Is your theory sound? Have you taken a step back?Did you ask for advice? Do you realize that this business can take awhile?
Design towards the sound in your mind and get to know your plugins better, most of all, spend a lot more time on it until you have the experience to do it quickly.
I feel like half my job is solving problems, and I find that creatively stimulating. I work mostly in games these days, which is much more technical than traditional post and it suits me well. But I love the challenge of knowing what I want something to sound like, but not knowing how to get there.
Also, there are so many different impediments to good sound aside from the purely creative problems, (time constraints, tool constraints, management issues, creative differences...) that when its just me banging my head against a purely sound issue, I love it.
If it's something like not having funds for or access to a mobile recording device (or a reasonably adequate one) to go record somewhere your standalone setup cables and mic's can't reach, then that's one thing.
Otherwise in my opinion there's no such thing as anything that limits my creativity except my own lack of imagination or problem solving skills (both which can be trained and curated).
And like several others have mentioned in this thread, I find that technical limitations usually force me to be more creative as well.
It's a matter of knowing the tools you have and their capabilities and the ways you can potentially use (and abuse) them.
If the Beatles did what they did with a 4 track then I think it's safe to say I should spend more time thinking outside the box and trying to innovate in times of perceived technical limitations.
Maybe try and find a film, game, or Tv show that's in the same vein as what you're working on and watch it. Keep an ear out for sounds you like and spend some time trying to think of how it/they was/were made.
Take your time and try absolutely everything you can think of. Especially if it seems silly and you're convinced it won't work.