Very Demanding Breastfeeding Baby

It is VERY common for toddlers to do this around 14-15 months. I think it has to do with them becoming more independent at 12 months then they get a little "scared" and want to reconnect with momma. How I got through it was to not sit down when I didn't want to nurse. I kept myself busy and would sling my big ol' boy around on my hip and play with him instead of sitting down because I knew he would instantly climb onto my lap and throw a tantrum if I didn't nurse him.

Both of my kids had a spurt of increased nursing right around 15 months or so, and it passed without me doing anything special besides meeting their needs. Personally, I thought they were feeling a bit overwhelmed by new independence and needed an extra dose of reconnecting with Mom.

Ah, yes. My first did this. It is a phase. I am starting it all over again w/ my 2nd who is 11 mths..
Like Abby said, try and keep busy. I was working a PT job at that time w/ my first and I'd come home tired and she would want to nurse and get down, nurse and get down, nurse and get down. Blah. It was not my favorite game to play.
Hang in there! It must get better (sorry my memory is foggy) because I continued to nurse till she was almost 3. I don't think I would have put up w that for more than another year. :)

she is getting soo smart...understanding what she likes and wants and obvioulsy likes/wants to be with you. You will need to work with her and distract her to somethign else. Perhaps not feeding her on demand...you will only do it at "such and such" times. It will take a few days, but your LO will get used to the schedule.
I wish I had more to tell you. I had to stop nursing at 4.5 months from working FT and my supply/demand were not matching up. Congrats on going this long!!

My DD would also nurse more with teething or illness or changes in her routine.

I would allow it for a time and then go back to the shorter sessions, redirect, etc. Even now my DD will put her hand on my skin and I know it really means "I need a connection with you" so I pick her up and hold her, talk to her, put down what I'm doing and give her a few more minutes. If you make a session shorter, try also increasing some cuddle time.

Separation anxiety, learning a bunch of new things, not seeing you as much as she'd like, and knowing that nursing time is the one activity that will calm, recharge, comfort and keep Mommy one on one time to herself.

If you deny her now - when there is truly no reason to force wean her unless you personally have an issue about it - when she's letting you know bluntly what she needs... you will cause her separation anxiety, tantrum/meltdowns and clinginess to increase.

It, like all of the short phases in your baby/toddler's life, this too will taper down to most likely 2-3 times until she self weans or you force her to.

I would see if something has changed -- is she is the same daycare room, same teacher, is she feeling ok? If the answer is that she's fine and nothing has changed, then I would say it is just a phase.

My daughter cut out some feedings on her own around 13 months, and then again around 16-17 months. I dropped her last feeding, before nap, at 17.5 months.

Either try to redirect her to something else, don't sit with her as much (the weather is getting nice, take her outside she'll find something interesting there), or just wait it out. I promise you, she's going to change a lot in the coming months and she'll be much more interested in things other than nursing.