Taylor Frankie Paul's still holding out hope fans might see her fall in love on "The Bachelorette" ... sharing a petition that calls for ABC to air the dang thing ... and it's got a lot of signatures.

The reality star posted the link to her Instagram story ... telling her fans she loved them for making it -- and admitting she signed it herself.

Taylor also shared the full demand letter from the petition ... which argues fans have been deprived of watching the star on a once-in-a-lifetime journey. Her fans say they've followed her and "know her heart."

The petition goes on to say taking away the season doesn't solve an issue -- it only silences TFP ... and viewers should be allowed to watch the show and form their own opinions of the star.

As of this morning, the petition has more than 16,000 signatures ... though it'll need a whole lot more to change the mind of ABC execs ... who opted not to run the season when it was supposed to air back in March.

Of course, the season was pulled after we published video of Taylor throwing a barstool at her ex, Dakota Mortensen, with her kid in the room. Taylor's been engaged in a custody battle with Dakota and her other ex, Tate Paul, in the months since the video came out.

Production sources told us "The Bachelorette" season was supposed to run starting in July ... but it didn't happen.

Instead, Utah's Department of Children and Family Services asked a juvenile court to find that Taylor's three children have been "abused, neglected or dependent."