v1      v2    v3
 ABC     0-10   3
 ABC    10-20   2
 ABC    20-30   4
 DEF    10-20  2.5
 DEF    20-30  3
 DEF    30-40  1.1
 DEF    40-50  2.7
 XYZ    40-50  2
 XYZ    >50   1

v1      v2    v3
 ABC     0-10   3
 ABC    20-30   4
 DEF    10-20  2.5
 DEF    20-30  3
 XYZ    40-50  2

dat[with(dat, ave(v3, v1, FUN=function(x) sign(x - cummax(x)))) != -1,]

#   v1    v2  v3
#1 ABC  0-10 3.0
#3 ABC 20-30 4.0
#4 DEF 10-20 2.5
#5 DEF 20-30 3.0
#8 XYZ 40-50 2.0