I've seen the same thing from the 'tape dots' and tape disks-- they tear, turn loose, the glue dries out, whatever... very unreliable.
I needed some material for making dots for a chute, and didn't have anything handy but duct tape. I cut some small 1/2 inch squares from the duct tape and attached it to the chute, and punched a small hole for the shroud.
What's good about duct tape is, the adhesive is VERY strong, and it's pretty long-lived too (won't dry out and turn loose after six months or a year) and duct tape is reinforced with a grid of strings, which greatly strengthens the attach point and spreads the loads. Once attached to a typical plastic parachute, the adhesive on the duct tape is SO strong it'll tear the whole corner off the parachute before it turns loose.
I advise using talcum powder to dust the chute, to make sure the adhesive doesn't stick the chute together-- the talcum 'seals' the edges of the tape...
I like it...
OL JR