This will do:
X <- read.csv(text="Day.Covered,SHIP_DATE,Warranty.Start.Qua.Yr,War.Start.Monthly,AssemblyDateUpdated,Warranty.End.Date,Warranty.End.Qur.Yr,War.End.Monthly
365, 06-04-2008 00:00, 08-Q2, 08-M6, 06-03-2008 00:00, 08-04-2064 ,64-Q2, 64-M4
1095, 08-17-2010 11:13:07, 10-Q3, 10-M8, 08-16-2010 12:09:57, 08-04-2064 ,64-Q2, 64-M4
731, 10-17-2012 00:00:00, 12-Q4, 12-M10, 10-16-2012 00:00:00, 08-04-2064 ,64-Q2, 64-M4
731, 01-04-2013 00:00, 13-Q1, 13-M1, 01-03-2013 00:00, 08-04-2064 ,64-Q2, 64-M4
1095, 06-13-2011 12:29:23, 11-Q2, 11-M6, 06-11-2011 11:25, 08-04-2064 ,64-Q2, 64-M4
1095, 03-16-2011 10:54:37, 11-Q1, 11-M3, 03-15-2011 08:14:40, 08-04-2064 ,64-Q2, 64-M4
1095, 06-18-2008 12:35:06, 08-Q2, 08-M6, 06-06-2008 10:51, 08-04-2064 ,64-Q2, 64-M4
731, 05-18-2011 00:00:00, 11-Q2, 11-M5, 05-18-2011 00:00:00, 19-11-2014 ,14-Q4, 14-M11
731, 10-22-2012 00:00:00, 12-Q4, 12-M10, 10-22-2012 00:00:00, 08-04-2064 ,64-Q2, 64-M4
730, 08-04-2009 17:43, 09-Q3, 09-M7, 07-31-2009 07:14:17, 18-01-2012 ,12-Q1, 12-M")
# Replicate X to have enough data for this example.
X <- X[rep(seq(nrow(X)), 100),]
# Partition the data according to quarter.
partitions <- split(X, X$Warranty.Start.Qua.Yr)
# Draw samples from each partition.
samples <- lapply(partitions, function(p) p[sample(nrow(p), nrow(p)/10),])