Is it possible for my tubes to come undone ?

Yes but not recommen: If it is for just another baby, ivf is a better choice.

Possible with method: It depends upon the tubal occlusion method. Fallopian tubes "plugged" from the inside of the uterus during hysteroscopy requires a follow up "dye study" to confirm the blockage one month after the procedure. Fallopian tubes "burned or clipped" can fall if the burn(cautery) is only in one location of the tube and the tube re-connects by later healing. Clips can come off if not secured properly.

No, but it can fail.: A tubal sterization does not come "undone". However, nothing is 100%, and a tubal sterization can fail. The failure rate for tubal sterization varies depending on how it is performed, and may be as high as 2%. The majority of failures with tubal sterizations will result in an ectopic pregnancy - which can be life threatening.