Dear  Parimanont,

Are you getting more than one non specific bands when you purify your desired DNA? 

I have faced similar problem before where, a single band used to appear after gel purification and used to migrate slower than my desired band. If you are not getting the band after PCR and only after gel purification, then it must be the same DNA which might have been denatured or nicked due to over heating in the gel extraction solution. You can follow the link for further clarification. 

https://www.researchgate.net/post/What_is_the_higher_molecular_weight_band_which_I_get_in_my_eluted_DNA

http://bitesizebio.com/13506/10-tips-for-better-dna-gel-extraction-results/

hi

you can used 1ul DMSO in PCR working solution and run Gradient PCR for deleted nonspecific band (2 kb) . Extension Time for Pfu 2 min and TaqGold 1 min as enogh / 35 cycle . be careful cut just 1 kb band on UV translumintor with out additional agarose.

good luck

Part of your DNA fragment may be supercoiled and therefore run at a different size on an agarose gel. Clone and sequence both fragments, then you will know.