Currently the only specialist magazine, Concertina & Squeezebox, is now permanently in abeyance. Back issues are much sort after, beautifully produced and a great read if you ever come across them.
The Center for the Study of Free Reed Instruments in conjunction with the ICA (see Section 10 for both) produces the Papers of the International Concertina Association once a year. These contain much superb scholarship.
The International Concertina Association has a quarterly newsletter for members which I find both interesting and informative.