There does not seem to be a direct mathematical analogue of Alfven. Nobody who has won a Fields Medal or an Abel Prize has made well-publicized complaints about how they have had an unduly difficult time with the peer-review system.
Some partial analogues have been mentioned in the comments. Louis de Branges had trouble getting people to take his proof of the Bieberbach conjecture seriously, but there was a clear reason: de Branges had a well-deserved reputation for making repeated but incorrect claims to have solved famous open problems. Fourier's work met with resistance, but there were some legitimate objections that some crucial arguments were not fully clear; while the Mochizuki saga is still in progress, it seems that the clarity of certain crucial arguments is still in dispute. Galois also ran into difficulties, although the story has been exaggerated, and Galois was not a recognized figure at the time.
Why there is no direct analogue of Alfven is an interesting question. There could be a difference in culture. Mathematicians will often complain privately of getting an unfair rejection, but complaining too loudly or publicly about the lack of recognition of one's own work is generally regarded as whining, and is frowned upon. Mathematicians also take the general attitude that there are three primary reasons for rejection: (1) the work is wrong; (2) the writing is unclear; (3) the result is not regarded by community as sufficiently interesting. The first two are considered to be the fault of the author, and mathematicians tend to take a somewhat fatalistic attitude toward the third. Under these prevailing assumptions, it is hard to be viewed as taking the moral high ground when voicing a complaint about a rejection.
One example of someone making a public complaint was Friedrich Wehrung (search for the word "rejection"). His primary complaint, however, was that the entire subfield of lattice theory was being looked down upon unfairly. Similarly, you can find public discussion about how the peer-review system unfairly treats certain groups of people. But again, if you're looking for an individual analogue of Alfven, I don't think there exists a very good example.