Will mutations become less freqent?

As others have said, there are three things that will affect mutation frequency:
1) diminishing returns for further fidelity
2) metabolic cost of increased fidelity
3) the benefit of having some mutation. This is kind of counter-intuitive, as most mutations are harmful or neutral, but (at least in bacteria) an increased mutation rate, particularly in stressful environments, can be a benefit. Some bacteria will increase their own mutation rate in response to stresses such as antibiotics or starvation. This is thought to provide a benefit - basically if you're going to die because of the stressful environment, then the risk of deleterious mutations is outweighed by the possible beneficial mutations. Provided you can pull the mutation rate back down when required.