Is it okay to ask the professor to let another student continue my Master's thesis topic next year? I am a Master's student in an Engineering discipline and I don't think the nature of my Master's thesis topic can be finished in time, realistically speaking (GUI development) and I have a month left. This project was actually proposed by the professor at the start of the year and I naively accepted it at the time. I am trying to suggest to the professor to let another student to continue my project next year and maybe improve on what is lacking and add more functionality. Is it common for projects to continue year after year?

There is one feature or function of the GUI which cannot be finished due to the lack of data quality. The data is actually collected and given to me by other PhD students, so it is not my responsibility to produce the data which is used for my project. The bulk of the main code and GUI has already been worked on and I will be able wrap up my project if this single feature could be dropped. However, if this feature is dropped, the scope of potential applications that my GUI can have becomes very limited. However, my supervisor is very keen on having this feature. What the PhD students are saying is that it is my responsibility to be able to work with low quality data and find solutions to go around it.
In the thesis there is usually a section called "future directions" or "recommendations" in which the candidate can lay out what can be done to improve or scale up the deliveries. Projects being developed in succession by different students are common, at least in my field (biomedical.)

As for whether you will get full credit, the question at its current state cannot really be answered because too many details are missing. For instance, has this likelihood of non-completion been on the advisor's radar? Or are you just dropping the bomb one month before the due date? Who has been causing the delay? Were any barriers or difficulties you faced raised and discussed? How incomplete is the project? All these can go into the consideration of your final grade, and that can of course include a potential "F."

I'd suggest, given the time limit, stop trying to get guessed answers on this forum. Instead, immediately schedule a meeting with your supervisor and make sure both are on the same understanding. Upon discussing with the advisor, come up with a list of tasks that need to be finish to make the Master thesis a reasonably stand-alone work, and complete it. Be realistic and don't be a yes-man (like what you did at the beginning); if the list grows too big, say so and trim it down together. Diligently follow up weekly and deliver the project.

Of course, if the project is grossly behind or substandard, you may want to prepare for an extension or walk away with a fail grade. The results of this discussion will vary depending how professional you have been behaving in this duration and perhaps many other factors. I wish you good luck and feel free to come back and update us by revising your question.