The problem could easily lie with either the way the musicians are playing the music or your inability to hear it and yourself clearly in the monitors. It may have nothing to do with your ability to keep tempo at all.
Many very talented and gifted vocalist who can sing karaoke or with a backing track they practice with, do just fine - until they try to sing the same song with a live band.
It is a common scenario that I see with singers who try to go from singing to a CD - to singing with a band. If you are not singing with a band - but rather singing live to a pre-recorded track, skip to the end.
The problem comes in because on a pre-recorded backing track, the musical cues are exactly the same each time you practice singing with them so you get used to exactly where the vocals are supposed to come in. Also, if you listen to a recording of a particular popular song, and then sing to a karaoke track modeled after that song, you have a reference vocal you can practice with that has the same musical cues that are on the karaoke CD.
By musical cues I mean things like a certain type drum beat, a forceful strum on a particular guitar chord, a certain bass riff, or sax riff. And with pre-recorded material, you have more opportunity to listen and practice until these cues become automatic.
With a live band, these cues will be completely different and may not always be the same with each performance. So, whereas on the CD you are used to hearing a particular saxophone riff right before you sing the bridge, maybe the band you are singing with, does not have a sax player so that cue is absent.
And with a live band, it's not as easy to get in as much practice as you can with a CD that you can play while you drive around in your car running errands.
I think you might just need to rehearse more with the band with the way they play the songs you will sing, and ask them to give you stronger musical cues for when the vocals need to come in. Maybe a symbol crash or a quick four strums on a particular power chord or something that stands out. And be sure they do it exactly the same each time.
In fact you might need to work with the band to create an arrangement of the music that you can follow and they can play consistently. Once the band has honed the arrangement and can play it consistently, record it so you will have something to practice to.
If you record it and still need help knowing where the vocals come in, have another band member sing some scratch vocals over the recorded music - just for the purpose of helping you with your timing. Use that as your "guide-vocal" track to listen to over and over until you can sing along with the guide vocals, and then start practicing singing along with the recording without the vocals.
It is very important that the drummer or percussionist and or bass player (if you don't have a drummer) maintain a consistent rhythm through the entire song. If you only have a guitar player, having him/her play in a more defined rhythm style may help with your timing. If you are playing the guitar yourself, it's easy to know when to sing. But if someone else is playing for you, there must be some easy to recognize musical cues to go by.
Finally, and this will apply whether you are singing with a band or singing to a backing track, you must be able to clearly hear the music and your vocals, in a monitor. I have seen many instances where singers who performed flawlessly in rehearsal, could not keep up at all in a live performance because they could not hear themselves and/or the music in their monitor (or did not have a monitor).
If there is no monitor available (which could be the case if you are performing solo and singing to pre-recorded music), try moving out in front of the PA speakers and face them so you hear what the audience hears, and hopefully everything you need to hear, to keep your timing in sync with the music.
If hearing yourself and the music is not a part of the problem, you might just need more rehearsal time, either with a recording, or the band - or both. Best of luck to you. You can do it!