It is wonderful that you don't give up on your students. 
I have a rule that says, if my students don't know something it is always, always a sign I haven't found a solution, yet! 
If she likes reciting poems it might be she is an auditory child and needs auditory stimulation. Using songs is a good strategy with such children. find ABC and number songs and only teach her to sing them. 

Some kids needs to learn the letter slowly. I always recommend using her name as a starting point. Can she recognize her name in a pile of other kids' names? When she recognize her name it is not really reading, it is photographing and most children can photograph easily, if toughs gradually about 50 words. 

Another option you have working on developing her visual perception long before you teach her the letters and numbers. for example: give her a page with many letters ( you can use a cross word page) and ask her to find all the F. circle one for her and ask her to find all the rest. It is not reading but visual development. 
You can do the same with numbers. 
The next level is finding similar words or similar numbers for example: 6696 and ask her to circle the odd one out. 

This is not reading but it is very important to start with that. 

Punishing is not a solution. She does not do it to annoy anyone. 

try this and tell me how it went. 
Ronit  

i still don't want quit and so hope you can suggest me.

I am glad it inspired you.
Studying for a test is an important skill but in the big picture, the real tests in life are different and it is a bit of waste of energy to teach kids to succeed academically.
What you are describing is parents neglecting the social life or the fun bit of life.
I wrote some articles about the importance of fun in parenting
http://www.ronitbaras.com/focus-on-the-family/parenting-family/the-fun-incentive/.

I agree with you. The whole philosophy of "Happy Parents Raise Happy Kids" is that whatever we want to give our kids, we have to own first.

here is another article about work life balance
http://www.ronitbaras.com/focus-on-the-family/parenting-family/work-life-imbalance/

Happy Parenting
Ronit
http://www.behappyinlife.com

I think that motivation is when you encourage kids to do something they are willing to do (even if it is hard) and inspiring is more of being a role model and modeling it.
When you are motivating a kid you need to find out that this is something he wants. If this is something you want, it is called "pushing".
With inspiring, you don't need permission to encourage, promote or motivate, you just there, doing what you believe is right, tell them about yourself and your choices that worked for you and and wait for them to take the lesson you are there to teach them.

I can see when motivating can work better and when inspiring can do magic - they don't have to be a contradiction. In fact, if you use both you will get better results.
Teach them to want, lots. Teach them to dream and want more for themselves teach them that stretches are what adults mean "growth" and that age has nothing to do with wisdom and growing inside. Teach them to believe that they can and they will.

Happy Parenting
Ronit
http://www.ronitbaras.com

thank you for this interesting information.
What is the optimal balance between motivation (making kids want to achieve something) and inspiring kids to relax and to pull themselves up for next achievements?

Thank you

Helen