In my opinion, don't wait and look for other opportunities in market. The simple reason is that the company do not take time to issue offer letter, if they decide to select the candidate. Because HR also know that it will delay the candidate joining and positon closure. HR have their own targets for position closure. therefore, if HR is not responding back on your mails or call , then it clearly means that they are not much interested in your candidature. But in future, if they will contact you , if they wish so.
Regular followup with them will let down your position and show desperation to get this job. It will break your chances of negotiation as well. Hence I suggest not to further followup with them and start looking for another vacancy.
This is my views