According to PewGlobal the US approval rating in Egypt went from 30% in 2006 to 10% in 2014.
Why did so many Egyptians change their opinions about the US?
In 2011 Egypt was one of several countries that experienced a resurgence of fundamentalist Muslim control from the Muslim Brotherhood. President Obama officially endorsed the Brotherhood over long time president and ally Hosni Mubarak who had made Egypt a secular state. Mubarak was forced out and in the following elections the Muslim Brotherhood won in a landslide, electing Mohamed Morsi.
Morsi quickly moved to make Egypt an Islamist country which sparked more protests and led to the Egyptian military taking over in a coup about a year after his election. In 2014 Abdel Fattah el-Sisi was elected as President after he resigned from the military, he was also the leader when the military took over from Morsi.
It is widely viewed that how Obama and Hilary, then Secretary of State, handled the entire situation was a massive blunder. The U.S. essentially let Egypt's government fall into a state of chaos for about 3 years, and was arguably complicit in doing so given their support to oust Mubarak.
I can not claim to know all the reasons that have caused those changes, but if we suppose the main cause is the relationship with the internal politics of Egypt1, the timeline is:
-> USA long standing support to Mubarak continues (Egypt is the second recipient of military aid by the USA)
-> Mubarak is deposed
-> Al Sisi's coup d'état. All charges against Mubarak dropped. USA and Western countries turn a blind eye (no demands for democracy, no threats of stopping military aid, etc.) towards the military coup and bloody repression of the Muslim Brotherhood.
So, most of the loss of public support matches the perceived support by the USA of the old dictatorship and the coup d'etat against the elected government; specially the last year data. Variations in the 2006-2011 period can be explained by the progressively lower support/opposition to Mubarak2; lower support to Mubarak meaning lower support of his sponsors.
Then again, this is just an hypotesis that should be taken with a grain of salt; a definite answer
1 I suppose some variation can be related to other issues of international politics; v.g. 2009 (the year a more "diplomatic" Obama replaces George H. Bush support for the USA) increases significantly. That same year, the confidence in the POTUS raises from 11% to 42%.
2 Check the question about the country economic situation.