I think you're burning up your flux.
ditch the batterns - you can make flux with borax (from the grocery store) and denatured alcohol. coat with the flux, crank up your torch - you want to be quick but not careless. I've never worked with a butane torch other than in the kitchen, if possible - no pointy flames - between pointy (hot) and bushy (cool'er).
Did you say - copper or silver ...hmmm don't see it. If silver, you want to heat the entire bangle - silver is an excellent heat conductor so while you're heating <---- here, the heat is moving ---> there. Once the whole piece gets hot (not red, just hot), the flux has stopped boiling, time to move the heat to the join.
I usually use my pick to place solder, but a good /easy way to solder a ring or bangle is to put the solder chip under the join and aim your flame just in front of the piece, bouncing the heat from the surface onto the bangle. Once the solder melts the pieces will sit down on the surface.
http://etsymetal.blogspot.com/2009/05/intro-to-using-boric-acid-flux.html