dog wont eat

Question
My 2 year old Portuguese Water Dog has been refusing to eat her food on and off for the past 8-12 months.  Prior to this time, she would sit barely able to contain herself until we released her to eat her food...which she promptly gobbled down.  She was fed 2x's day, 1 cup each time, EVO dry dog food.  She has been on this same food since she was a puppy.  Now she will wait quite some time to go up to it, will sniff it & walk away.  She may repeat this several time, eat none of it, a little of it, or all of it. She has gone 24 or 48 hours without eating. A few times she has vomitted yellow bile, I believe from having empty stomach/excess acid with not food in it.  Otherwise, she doesn't appear ill, no gurgly stomach, still energetic as ever. She never refuses a treat.  Also, if a piece of kibble drops on the floor, she will usually eat that too. It has become frustrating and also concerning for us.  My expectation is that she will eat her food when I put it down.  We have tried several different strategies to remedy:
1) As recommended on clicker training website (dragonflyllama.com), we put her food down, if she sniffs & walks away take it up.  Offer food to her again at next meal time.  If she sniffs & walks away take it up.  Next, offer less food.  With the thought, she won't starve herself, she will eat eventually.  However, we have been on/off consistent with this.  How long is too long without food? I have let her go as long as 48 hours.  (That happened today & then I made her some rice/chicken concerned I haven't wanted her to go longer than that..and make herself ill, hypoglycemic etc...she gobbled it up).  
2) We tried cutting food amount in half, giving her food toys as "reward" after eating her meal from her bowl.  Various ones by Busy Buddy that you stuff with kibble & she bounces around to get food out.  That worked for a time.
3) We have tried mixing her food with water or canned pumpkin.  Also works for a time then she begins refusing food.
4)Most recently tried changing her food schedule to once/day only for the past month....thinking perhaps, metabolism is down, not needing as much food now that she is not a growing puppy.

I believe this is a behavior issue-but I'm not sure how to address it.  I know our consistency is an issue.  Partly my concern is, we need to know we are doing the right thing in order to stick with it.  Emma's life has changed about 14 months ago when we had a little boy...and her routine was thrown way out of wack while he was an infant.  We also used to do a fair amount of clicker training, which she enjoyed.  However, she knows the basics & we don't do that much at all anymore.  
We would appreciate any guidance you can give & are happy to provide more information.  My hope is that we will find a strategy that is safe, that we feel comfortable being consistent with, that she will eat consistently when fed.

Answer
The first thing to do is rule out any possible medical cause for her inappetance.
While I don't agree with pandering to dogs who simply want to get chicken and rice and know how to manipulate their owners to do it, I do rotate my own dogs' foods fairly regularly (I mix two foods for a day or two so the change isn't sudden), so that they get variety without me having to resort to bribery with chicken.  If you think about a dog's wild diet, they might eat rabbit one day, mouse the next.  No single manufacturer knows everything, and even the best foods sometimes disagree with a particular dog - sensitivities can develop over time with a particular food or ingredient, too.  There are some ingredients that tend to offend more than others - chicken is one of them (wheat and soy are others).  So, some owners opt for a different protein source. (The only way to know for sure if a dog has a food allergy is an elimination diet or testing.) For example, my hound is sensitive to chicken, so I might feed him California Natural herring & potato versus a food that uses chicken and rice.  

Occasionally, a dog will have a tummy ache and make an association that a particular food might have been responsible!  A different dog food that smells different might solve that problem.  As you say, however, inconsistency in expecting her to eat her dog food might also contribute - after all, she may simply have learned that if she just holds out long enough, she will get real chicken!  When you offer a different food for variety, perhaps it should just be a different dog food, but not make the  change at the same meal time she refuses food - put the new food down at the next meal.  If you have left her food out for long periods of time ("she takes a long time to go up to it"), that could be the problem, too.  Put it down, let it be there about 1/2 hour - take it away till next meal, but NO treats or other temptations.  

Make sure your dog has a safe secure place to eat - if your little boy is a toddler, and milling around the kitchen, or has accidentally scared her there in the past, she may not feel safe eating there.  

Go back to paying her some attention - she may have learned that the only way to have you do that is to fail to eat!!!  No one is so busy that they haven't five minutes here or there to do some training or play with the dog, and it's also great training for children to be aware that mommy pays attention to the pup's needs and they sometimes have to wait.  That's another way for kids to learn self control:-)))  Teach her some tricks - your excitement over her progress is a great remedy for depression, which can also affect dogs.  

If you need a list of other good foods, visit
The Dog Food Project online or Whole Dog Journal's February issue.