if you have been in public sector long enough, it isn't that hard to get offer as long as you don't have a bad track record and the job is generic enough.

having 5 public organizations not willing to offer increment means he is close to or above the bar/mid-point of his job level and so far he hasn't been able to demonstrate and convince anyone that he is qualified for bigger job responsibility or has the cep to show that he still has room to grow.

if u give me few months of just whacking whatever jobs are on careers.gov i am quite confident of getting at least 3 offers also, but just not good jobs on favorable terms. not meant to boast, but those in public sector long enough will know what i mean.