You are sensible, and want to wash your Jiu Jitsu belt after every session.
Jiu Jitsu knowledge and your Qi do not accumulate in your unwashed belt. Accumulating ringworm, staph and hep B might, no matter how good the mat hygiene at your gym.
Your problem? The stripes on your belt are duct tape. Not real good in the washing machine, right?
You and your significant other do not have the sewing skills or inclination to sew on something more elegant or permanent.
Your solution: strapping tape, like you use for taping up your fingers. Stays on after multiple washes, no problem. If you have the red bar on your black belt, or the black bar on your different coloured belt per the IBJJF official requirements, you can use the easy-to-get white tape. I use the 1.25 cm width.
Should you have no black bar, or want specific other colours, try kinesiology tape, which comes in many colours, though blue, purple, black and brown (well, beige) are easily obtainable, which should satisfy most adults. You should be able to get all the kids' colours except possibly grey. You may have to trim it to a narrower width than that in which it is sold, but it still beats fiddling around with needle and thread or a sewing machine.
The picture above shows my belt after about ten jiu jitsu sessions and washes - an intense, one wash, two rinse, spin cycle - with a stripe of white strapping tape on one end and one of black kinesiology tape on the other. Some fraying, no loosening. If, and when, it does start to lift off ... I'll replace it with a new piece of tape.
Try it. It works!