A few thoughts for you:
Are there other new kids in her class, or is the class almost entirely kids her age who have been in this same preschool together for a couple of years? Some children start preschool as young as two and a half, so some of her classmates might have been together for what seems to them like their entire lives. If that's the case, what she is experiencing may not be intentional "meanness" of kids excluding her but instead could be the other kids simply doing as young kids do and sticking to what's familiar. She also is coming in very late in the typical "school year" as well.
I'd talk with the teacher (without your daughter present, and when the teacher has time to talk -- not a quick word in the hallway at pickup time) about exactly how the teacher "encourages the other children to play with her." The teacher may need to be more proactive than just encouraging; she shouldn't be forcing anyone to play with anyone, but she does have the ability to tell student Sally, "Sally, I'm putting you and KellysDaughter in charge of the sand table today! You get to be the ones to put out the sand toys and tell everyone when the table is ready!" In other words - the teacher may need to do more to pair your child one at a time with other kids to do tasks and make it seem like the biggest treat ever. Giving a child responsibilities and talking up those responsibilities can be a big help.
Ask the teacher if SHE thinks that the fact your daughter is 4.5 and new to preschool, and has come in late in the school year, is a factor here. I think it may be.
And remember - she has only been doing this twice a week for one month! That's about eight class sessions -- not much at all. She needs time to adjust and yanking her out now will not give her that time and will turn her into the new kid all over again at a new school. Bear in mind too that when a child her age is upset, she is indeed upset, but...she is also at an age where any upset is magnified into a major issue. If YOU let her see that you too are upset on her behalf she will pick up on that and it will get worse. Tell her you're sorry she feels that way, but don't be overly gushy along the lines of "Oh my poor precious, those girls are not nice at all" etc. -- that will feed her sense that she's upset.
You can help at home too by scheduling play dates with kids from preschool. This really does help, believe me. Remember that kids this age do not do well in threes -- two will focus on each other -- so keep play dates one on one. Are you able to hang around and meet other parents? It's very valuable to your child if you can make acquaintances with other moms and therefore get your child together with theirs outside school. If she's likely to stay at this preschool for another year, you really do need to get to know other parents.
Also, it's possible that she is going too infrequently and for too long when she does go. That may sound odd at first but think about it. My friend's son had a hard time with preschool at first and his mom realized it was because he only went two mornings a week, and there was a five-day gap between one day (Thursday) and his next school day (Tuesday). He just didn't adjust to the idea that school was coming up days and days from now -- he couldn't really think that far ahead. Then when the day for school did arrive, he would have a tough and teary day. He actually did much better when he went four days a week and there were no more than three days between his last school day and the next one; he could settle into the routine of it and frankly had less time to dread the next school day.
He also (like my child and many others) went only for half-days, not full days. Five hours is pretty much a full day, and a big adjustment for a child like yours who has had no preschool at all and is older - she is used to having her own schedule at home and now has what feels to her like an eternity between dropoff and pickup. Is there an option for a shorter day but more frequent days of preschool? I would not push five days a week on her at all, it's not necessary, but three shorter days instead of two longer ones could give her more of a routine to slip into and a better sense that preschool is not so very long each day.
She is "asking every night and morning if she'll be going to school that day," you say -- which indicates she is totally uncertain about when school really is going to happen, and she sees it as something that happens TO her instead of something she DOES herself like a big girl. She needs the right schedule plus a sense of ownership that school is her special place.
I would really look into adjusting the schedule, getting her together with classmates outside school, ensuring she is not just encouraged but given responsibilities alongside other kids, and talking with the teacher.