While I am not an expert on Oregon law, I believe that the cause for denial was faulty - Oregon is a "shall issue" state with only a limited number of exceptions. Not being in the area 2 days per week is NOT one of those so enumerated.
Oregon will only issue permits to people who are residents of states that border Oregon. Those states are Washington, California, Idaho and Nevada. A non-resident from the states listed can go to any sheriff in Oregon and apply. The sheriff's office from Grant county has been found to have very good customer service and appropriate policies. They can be found at: http://www.oregonsheriffs.org/grant/index.shtml.
In 1989, Oregon also adopted a non-discretionary policy for issuance of handgun permits. The requirements were similar, though not identical to those we have already seen. The applicant must be over 21; must be a resident of the county where the application is made; must have no outstanding arrest warrants; must be "not free on any form of pretrial release"; must have demonstrated competence through any of a number of firearm safety classes; must have no felony convictions; must have no misdemeanor convictions or mental hospital commitments in the preceding four years; and must not be prohibited by a court from owning a firearm for mental illness