I keep small rolls for lightweight trips. No matter what, it always loses too much stickiness for me if it's wrapped around something else or on sticker backing.
I just try to use the full size rolls around the house. With three young boys, I can use up half of a roll pretty quick and save the rest. They're always needing a "super-duper bandaid!"
If you use wax paper, to create precut strips, be careful what you choose to use. I used generic cheap wax paper and it fell victim to the adhesive and the tape did not peel off cleanly, rendering it useless. Going to try the label paper moving forward. My suggestion is to test peeling it off prior to heading out!
I have 2 rolls of tape. One old and one new. I pre wrap my feet before a hunt and have a much smaller old roll of tape in my pack. Eventually, the new roll becomes the old roll and I buy a new roll.