Make the sub gift badges permanent.
If you gift 100 subs and they run out, your badge disappears forever unless you gift a sub every month. But if you gift 1 bit, in 5 years you will still have that (ugly) bit badge. That sounds unfair to me. Make the sub gift badges permanent, or make it so that it will stay 1 month for every sub gifted (so for 10 gifted subs get the 10 gift subs badge and keep it for 10 months).
I thought they were already forever
Just a heads up, you can choose what badge(s) to display by clicking the cogwheel at the bottom of a chat and selecting your name under "Chat Identity". Hope this helps!