You can tear off a piece of masking/duct tape and tape the wire down onto the solder point. (Masking/duct tape won't short anything, it will just stick the wire onto the solder point.
http://www.3m.com/CA/english/centres/home_leisure/duct_tape/ If you prefer transparent tape, then that is good as well but it might not be strong enough to stick the wire on.
Normally soldering will almost always stick wires once the solder is hardened. Make sure you apply a decent amount and hold the wire onto the point while doing so. Seems strange how you got the other points to solder properly.
