This is the 265th most frequent Turkish word.
zor
Difficult; force.
In this sentence, 'zor' is used as an adjective meaning 'difficult' to describe the problem.
Bu problem gerçekten zor.
This problem is really difficult.
Here, 'zor' is again an adjective, this time describing the gradual difficulty increase in the work.
Sabırlı olmaktan başka çaremiz yok; ama işimiz giderek daha zor hale geliyor.
We have no choice but to be patient; yet our work is becoming increasingly hard.
In this context, 'zor' is part of the expression 'zor ikna olmak', implying a situation of being convinced with difficulty.