For me, those two things really feel like two different manifestations of the same feeling. It's not hard to get from one to the other; sometimes an audience is all I need to start feeling frustrated instead of determined. On the other hand it's rare for me to feel frustrated on my own.
For example, I've always considered myself good at the intractable emergency technical problems sysadmins tend to run into. Somehow one of my best professional memories at Mitel is spending a weekend in the server room with two broken Raidzone filers which lost multiple IDE disks during a bunch of power cycling brought on by a poorly-executed UPS switchover. They had the same data on them, one more up-to-date than the other, but had interesting combinations of failing drives, incomplete RAID 5 parity, and corrupted ReiserFS filesystems. It took the whole weekend to get things back up but they were ready for Monday morning.
But if I'd had someone sitting beside me that weekend I wouldn't have had the presence of mind to just plow through; I'd just have been frustrated at the whole thing. I notice this at home; if something's broken at work, I'm a lot better at fixing it if nyxie isn't here. If she is I end up talking to her about how the problem makes me feel -- or at least expressing that I am hard at work doing something annoying with body language and so on -- and end up actually feeling annoyed at the problem.
And today was a "converting determination into frustration" day at work, a weird MySQL problem that was not straightforward to solve, slowed down the app significantly on a busy day, and which kept involving discussions about how bad it was and how important it was to fix it instead of actually fixing it -- which Taavi and I finally did, working straight from our hunches even when things weren't looking promising.
At first I thought the frustration problem was because when I'm talking to someone while working on a problem I end up talking about how I feel about the problem, and that lends itself to negative thoughts, but that's not what happened today. It's true that talking to someone technically about the problem doesn't have the same effect. It could just be that it's expending effort towards something other than the thing I was determined to do. It's the difference between thinking about the problem, and thinking about the situation I'm in facing the problem -- even if the feelings about the situation are someone else's.
And in those terms it becomes familiar.
The thing that converts determination to frustration is creeping doubt: wondering whether or not the problem is solvable, or thinking about how having to solve the problem is going to affect me, instead of trying to find the solution. Wishing the situation were different instead of trying to accept the challenge of making it so. That's good old clinging.
So turning frustration back into determination is just a case of letting go of how I feel about the problem, and looking at the problem! Somehow I think it might be harder than that, but that seems like a good start.
Years ago (wow, I was on LJ in 2002?) when things were rough I had this little bit of Hebrew at the bottom of the main page of my website: גזי It stands for gam zeh yaavor, this too shall pass, which was sort of my motto at the time. I hadn't thought about it for a while, but it served me well then, and I bet it will again.