Cannot see in short distance after a LASIK surgery. Is this normal?

If you are over the age of 40, you are likely experiencing presbyopia.  Presbyopia occurs around the age of 40 where we slowly lose our ability to focus on objects up close and as a result we start needing to wear reading glasses to help us see.  Refractive surgery such as LASIK or PRK may correct each eye for one distance e.g. distance or near but cannot correct for both.  

There are a few important details that you don't include in your question: how old are you? Why did you have your LASIK redone? If I had to venture a guess, I imagine that you are over 40 (and presbyopia which means you start losing the ability to see things up close with age) and you had your LASIK redone because they left a little myopia and you weren't perfect at distance. No question about it, LASIK cannot give you all ranges of vision over the age of 40. Getting those ranges would entail another surgery: refractive lens exchange with presbyopia lens to give you the range you are looking for.