What if my landlord exterminated can I still sue him if he refusing to continue to exterminate properly?

Not necessarily. Other steps to follow first and depends on damages, if any.

Unless the lease says otherwise, you probably have a claim against the landlord. Plus, you probably have justification to leave the property.

I am assuming that you are stating that your landlord has failed to properly exterminate the home and that you have an insect problem. There is not bright line rule as to how many times exterminations must happen. It should be done enough to properly cover the home. You also need to look at your local health and building codes. Some codes, take away landlord responsibility for this depending on the number of units in the premises (if its a home vs. an apartment building). If you are in North Carolina and you have a bad insect infestation, you need to first write to your landlord and give him a reasonable time to fix the problem. If the problem is not fixed, then you can sue him in Small Claims Court. You would sue for rent abatement...this means that you believe the home is worth less than what you are paying and you can get a refund of the difference and an order lowering the rent until the problem is fixed. Note: you have to convince the judge/magistrate that the home is worth less due to the infestation. It will matter how severe it is, if it is bad in normal conditions or only occurs at specific times such as rain, and what type of insects are there. These are difficult claims to pursue unless the infestation is very bad.