If you write code professionally, you will have days where you find yourself utterly stuck on a problem. In fact, some days coding feels like trying to wade through quicksand: The harder you struggle to get out the more stuck you find yourself. Getting into one of those situations where you are stuck and can't find a way out is perfectly normal. And it is perfectly acceptable for a professional programmer as well. Every programmer finds themselves in those situations from time to time. Getting stuck is a natural part of creative work like programming, and as such we must simply accept that we get utterly stuck now and then. The important part is what you do about it. As with quicksand the trick is to relax a bit, sit back, and realize that you need to seek help. Not all programmers realize this, but the best ones do.
When faced with an insurmountable problem some programmers just press on and try to work through it. That usually means they start thrashing; they run around in circles without getting anywhere. While this might keep them warm, and even make them seem really busy and hard working it doesn't help the project. Some programmers sort of lose interest and start surfing the web or drinking inordinate amounts of coffee. That doesn't help the project either. To get out the situation you're stuck in, you probably need help - I know, I always do. So seek help.
Seeking help can mean a number of things depending on the problem you're facing. If the problem is on the code level try asking a teammate to come and pair with you - or if you're already pairing, ask to switch pairing partner - that extra set of eyes usually helps. If the problem is a design issue, again ask a teammate to help you out, but get up from the keyboard and go to the white board. Again the extra set of eyes - or even just the process of explaining the problem - usually helps. If the problem isn't technical but has to do with say access to the right tools, the right level of support from third parties, or unrealistic deadlines, ask your project manager for help. And if he or she is not able or willing to help, don't be afraid to escalate the problem to his or her boss - it's the professional thing to do. As I said: Seeking help can mean a number of different things.
But whatever you do, don't just stay stuck. Do something about it.