Are there any problems with the main-stream method of New Testament textual criticism, often called Reasoned Eclecticism? Yes, there are growing problems.
Have these problems reached a point at which the whole method deserves to be abandoned? You be the judge.
A friend of mine was challenged on a university campus with the following four questions:
Do you have the original copies of the Bible? My friend answered, No. Do the manuscripts all agree 100%? My friend answered, No. Do you have a system to trace the ancestry of the manuscripts? My friend answered, No. Do you have a mechanism to destroy false copies? My friend answered, No. "There”, said the fellow, “You believe that your Bible is from God, but you have a corrupted Bible. God would not have allowed this to happen if Christianity was the true religion”.
However, as my friend explained, strangely enough, the fact that we have to answer No to each of these questions (with one more question of our own thrown in) actually ends up strengthening our confidence in the NT.