He appointed his daughter to the US Senate and it appeared he was doing so on because of nepotism, and the economy is also doing badly in AK. Lastly, he or his daughter have been in gov't for years and haven't been able to past ANWR.
Let's break this down.
1. Yeah he did appoint his daughter to the Senate and it probably was because of nepotism. So +1 for you.
2. Before the pipeline shutdown Alaska was doing great. It had a huge budget surplus and was actually going to give a higher payment to Alaskans, from the dividends of the permanent fund, then the year before. I think Alaska always ranks in the top 15 richest states in the Union. Of course the pipeline shutdown will hurt the economy enormously but Alaska's economy before then was doing quite well, much like other independent petro-states such as the UAE, Saudi Arabia or Azerbaijan.
3. What the hell would ANWR have to do with the Governor? Most Alaskans know that even the stupid blumbling fool Murkowski and daughter have made that a priority. You can't be elected to office in Alaska without making ANWR drilling a priority. Most Alaskans blame the failure of ANWR proposals on enviromentalists from the "Lower 48" who don't get Alaska's needs and to faraway Washington officials who could care less about Alaska. The backlash against Murkowski isn't because, as Governor, he hasn't done anything about ANWR but mostly because he has been shown to be an incompentent Governor and has bumbled the issues most Alaskans are concerned about, local Alaskan problems.