Once Caitlin had passed away Julian took off Caitlin's necklace in hopes of bringing her back to life (which he did), but instead of putting it back on he stood there and let her escape. Why?
Well, Julian first checked her wound watching it heal. Once that was done he stood there stunned for about half a second, probably because he feared the healing wasn't actually going to work after she was already essentially dead. Caitlin is his kinda/sorta girlfriend after all, so he did it as a reckless maneuver, but that doesn't necessarily mean he expected it to actually work this late in the process.
When the camera pans to Caitlin's face right after that, she opens her icy eyes and when everybody approaches her - probably with the intention of putting the necklace back on - Killer Frost defends herself and sends out her cold air shockwave and throws everybody away to prevent that.
Killer Frost wants to live after all, which she cannot if Caitlin gets back in control, so she drives Caitlin's friends who are her enemies away from her body.
Additionally, the timeframe is actually pretty narrow for it to be put back on:
After Julien rips the necklace off, Cisco tries to stop him and actually ends up with it clutched in his hands, moving around and grieving, so it is actually at the wrong end of the bed when it is needed, because Cisco goes to the nearest free point of the bed when Caitlin has a pulse again, which is the bottom end. Therefore he would have to run around either Julien or HR who are standing on both sides of the bed. Even not stunned he would have had a hard time doing that.
Julien lifts away the bandage, than Killer Frosts takes her first cold breath and opens her eyes. Julien and Cisco stare in shock for 3 seconds (within that timeframe Julien manages a kind of wide-eyed-oh-darn-what-have-we/I-done gulp -- if it is shown in real time, it could be even less, because both Julien and Cisco get a close-up shot, as does the heart monitor going crazy, of 1 second each, so their being stunned could happen at the same time, but shown individually) and they are thrown across the room.
After that it is anybody's guess where the necklace ended up, because it doesn't seem to be in either of Cisco's hands anymore.
Because right now Caitlin is Killer Frost, and she has become too powerful for Team Flash to approach her to put the necklace back on. I think even Barry can't do it. But if he was as powerful in the show as in the comics, I think he could.