Do you have it wrapped in the correct direction? With your hands on the bars, in the drops, or on the tops, the leverage from your hand to your arm around the bars should be in causing the tape to actually tighten around the bars. At the transition from the drops, over the hoods and onto the tops, it is sometimes easy to get started in the wrong direction when wrapping around the hoods such that with your hands on the tops, it will actually unwrap the bar tape. The direction of the tape edges on the left and right side of the bars should make a "V" with the point being towards your stem or top tube, and
No need for extra adhesive or double sided tape, they will just fight you when you want to change the bar tape and make a mess. Sometimes there just comes a time when the tape is stretched and worn and time to replace.
Hope this helps