I've not been able to find specific numbers relating to the party in office but attached is an article on the shrinking middle class by decades...
http://www.npr.org/2016/07/07/484941939/a-portrait-of-americas-middle-class-by-the-numbers
It breaks down the numbers from 1971-2015.
'71-'81: Down 2% from 61% to 59%. '71-'74 Nixon (R), '74-'77 Ford (R), '77-'81 Carter (D).
'81-'91: Down 3% from 59% to 56%. '81-'89 Reagan (R), '89-'91 HW Bush (R).
'91-'01: Down 2% from 56% to 54%. '91-'93 HW Bush (R), '93-'01 Clinton.
'01-'11: Down 3% from 54% to 51%. '01-'09 W Bush (R), '09-'11 Obama.
'11-'15: Down 1% from 51% to 50%. '11-'15 Obama
As I mentioned above, this does not break it down into specifics as to when it happened within the decade and who was in office at the time, but the in two decades with 3% drops in the middle class, 17 of the 20 years had a Republican in office, or 85% of the time America saw the sharpest declines in the middle class.
I'm not saying your wrong, as I don't have stats to back up the decline based on who was President, and honestly I don't know that it matters. Based on these numbers it's a continuous decline regardless of which party is in office.
So, what's the real fix?