re: "It's hard to beat a team twice."

In all rematches since 1950, 60% of the teams won both games.

All rematches since 1950:
1950s
San Francisco beat San Jose State (39-2) on Sep 21, 1951 AND again (42-7) on Oct 12, 1951
Iowa beat Oregon State (14-13) on Oct 6, 1956 AND again (35-19) on Jan 1, 1957 at Rose Bowl (Pasadena, CA)
Oregon beat Washington State (14-6) on Oct 3, 1959 AND again (7-6) on Nov 14, 1959
Louisiana State beat Mississippi (7-3) on Oct 31, 1959 BUT Mississippi won (21-0) on Jan 1, 1960 at Sugar Bowl (New Orleans, LA)

1960s
San Jose State beat Pacific (16-0) on Sep 22, 1961 AND again (29-26) on Nov 11, 1961
Southern Mississippi won AT Memphis (20-14) on Oct 10, 1964 AND again (20-18) on Nov 21, 1964 at Jackson, MS
Michigan State beat UCLA (13-3) on Sep 18, 1965 BUT UCLA won (14-12) on Jan 1, 1966 at Rose Bowl (Pasadena, CA)
Quantico Marines beat Camp Lejeune (36-12) on Oct 30, 1965 AND again (14-7) on Nov 13, 1965
Wofford beat Furman (13-7) on Sep 28, 1968 AND again (21-7) on Nov 28, 1968
Wofford beat Furman (49-7) on Oct 11, 1969 AND again (31-21) on Nov 27, 1969

1970s
Ohio State won AT UCLA (41-20) on Oct 4, 1975 BUT UCLA won (23-10) on Jan 1, 1976 at Rose Bowl (Pasadena, CA)
Nebraska beat Oklahoma (17-14) on Nov 11, 1978 BUT Oklahoma won (31-24) on Jan 1, 1979 at Orange Bowl (Miami, FL)

1980s
UCLA won AT Michigan (31-27) on Sep 25, 1982 AND again (24-14) on Jan 1, 1983 at Rose Bowl (Pasadena, CA)
Southern Illinois won AT Indiana State (34-21) on Oct 22, 1983 AND again (23-7) on Dec 3, 1983
Indiana State won AT Eastern Illinois (17-13) on Oct 29, 1983 AND again (16-13) on Nov 27, 1983
Michigan State beat Southern California (27-13) on Sep 7, 1987 AND again (20-17) on Jan 1, 1988 at Rose Bowl (Pasadena, CA)

1990s
Central Michigan beat Nevada-Las Vegas (35-23) on Sep 10, 1994 BUT Nevada-Las Vegas won (52-24) on Dec 15, 1994 at Las Vegas Bowl (Las Vegas, NV)
Toledo won AT Nevada (49-35) on Sep 23, 1995 AND again (40-37) on Dec 14, 1995 at Las Vegas Bowl (Las Vegas, NV)
Florida State beat Florida (24-21) on Nov 30, 1996 BUT Florida won (52-20) on Jan 2, 1997 at Sugar Bowl (New Orleans, LA)
Notre Dame won AT Louisiana State (24-6) on Nov 15, 1997 BUT Louisiana State won (27-9) on Dec 28, 1997 at Independence Bowl (Shreveport, LA)
Alabama won AT Florida (40-39) on Oct 2, 1999 AND again (34-7) on Dec 4, 1999 at SEC Championship (Atlanta, GA)
Texas beat Nebraska (24-20) on Oct 23, 1999 BUT Nebraska won (22-6) on Dec 4, 1999 at Big 12 Championship (San Antonio, TX)
Marshall won AT Western Michigan (31-17) on Nov 13, 1999 AND again (34-30) on Dec 3, 1999 at MAC Championship (Huntington, WV)

2000s
Western Michigan won AT Marshall (30-10) on Oct 5, 2000 BUT Marshall won (19-14) on Dec 2, 2000 at MAC Championship (Huntington, WV)
Florida beat Auburn (38-7) on Oct 14, 2000 AND again (28-6) on Dec 2, 2000 at SEC Championship (Atlanta, GA)
Oklahoma won AT Kansas State (41-31) on Oct 14, 2000 AND again (27-24) on Dec 2, 2000 at Big 12 Championship (Kansas City, MO)
Tennessee beat Louisiana State (26-18) on Sep 29, 2001 BUT Louisiana State won (31-20) on Dec 8, 2001 at SEC Championship (Atlanta, GA)
Texas beat Colorado (41-7) on Oct 20, 2001 BUT Colorado won (39-37) on Dec 1, 2001 at Big 12 Championship (Dallas, TX)
Oklahoma beat Colorado (27-11) on Nov 2, 2002 AND again (29-7) on Dec 7, 2002 at Big 12 Championship (Houston, TX)
Louisiana State beat Georgia (17-10) on Sep 20, 2003 AND again (34-13) on Dec 6, 2003 at SEC Championship (Atlanta, GA)
Maryland beat West Virginia (34-7) on Sep 20, 2003 AND again (41-7) on Jan 1, 2004 at Gator Bowl (Jacksonville, FL)
Miami (FL) won AT Florida State (22-14) on Oct 11, 2003 AND again (16-14) on Jan 1, 2004 at Orange Bowl (Miami, FL)
Miami (OH) beat Bowling Green State (33-10) on Nov 4, 2003 AND again (49-27) on Dec 4, 2003 at MAC Championship (Bowling Green, OH)
Auburn won AT Tennessee (34-10) on Oct 2, 2004 AND again (38-28) on Dec 4, 2004 at SEC Championship (Atlanta, GA)
Miami (OH) beat Toledo (23-16) on Nov 2, 2004 BUT Toledo won (35-27) on Dec 2, 2004 at MAC Championship (Detroit, MI)
Akron beat Northern Illinois (48-42) on Sep 24, 2005 AND again (31-30) on Dec 1, 2005 at MAC Championship (Detroit, MI)
Texas beat Colorado (42-17) on Oct 15, 2005 AND again (70-3) on Dec 3, 2005 at Big 12 Championship (Houston, TX)
Southern Mississippi beat Houston (31-27) on Oct 14, 2006 BUT Houston won (34-20) on Dec 1, 2006 at CUSA Championship
UCLA beat Brigham Young (27-17) on Sep 8, 2007 BUT Brigham Young won (17-16) on Dec 22, 2007 at Las Vegas Bowl (Las Vegas, NV)
Purdue beat Central Michigan (45-22) on Sep 15, 2007 AND again (51-48) on Dec 26, 2007 at Motor City Bowl (Detroit, MI)
Oklahoma beat Missouri (41-31) on Oct 13, 2007 AND again (38-17) on Dec 1, 2007 at Big 12 Championship (San Antonio, TX)
Central Florida beat Tulsa (44-23) on Oct 20, 2007 AND again (44-25) on Dec 1, 2007 at CUSA Championship
Boston College won AT Virginia Tech (14-10) on Oct 25, 2007 BUT Virginia Tech won (30-16) on Dec 1, 2007 at ACC Championship (Jacksonville, FL)
Air Force won AT Houston (31-28) on Sep 13, 2008 BUT Houston won (34-28) on Dec 31, 2008 at Armed Forces Bowl (Fort Worth, TX)
Navy won AT Wake Forest (24-17) on Sep 27, 2008 BUT Wake Forest won (29-19) on Dec 20, 2008 at EagleBank Bowl (Washington, DC)
Boston College beat Virginia Tech (28-23) on Oct 18, 2008 BUT Virginia Tech won (30-12) on Dec 6, 2008 at ACC Championship (Tampa, FL)
Georgia Tech beat Clemson (30-27) on Sep 10, 2009 AND again (39-34) on Dec 5, 2009 at ACC Championship (Tampa, FL)
Nebraska won AT Washington (56-21) on Sep 18, 2010 BUT Washington won (19-7) on Dec 30, 2010 at Holiday Bowl (San Diego, CA)
Auburn beat South Carolina (35-27) on Sep 25, 2010 AND again (56-17) on Dec 4, 2010 at SEC Championship (Atlanta, GA)

Beat Opponent AGAIN: 30 (61.224%)
Got Beat 2nd time: 19 (38.776%)
Won AT opponent 1st game AND WON REMATCH: 10
Won AT opponent 1st game but LOST REMATCH: 7

ETA: re-ran parser accounting for ties.