In stead of creating objects in the environment with a specific, month dependent, name, I would use a list of objects where month is used as name.
dat = lapply(1:4, function(x) letters)
names(dat) = c("Jan","Feb","Mar","Apr")
> dat
$Jan
 [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" "q" "r" "s" 
[20] "t" "u" "v" "w" "x" "y" "z"                                                 
$Feb                                                                             
 [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" "q" "r" "s" 
[20] "t" "u" "v" "w" "x" "y" "z"                                                 
$Mar                                                                             
 [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" "q" "r" "s" 
[20] "t" "u" "v" "w" "x" "y" "z"                                                 
$Apr                                                                             
 [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" "q" "r" "s" 
[20] "t" "u" "v" "w" "x" "y" "z"  
Saving this list can be done easily using save(dat). If you are keen on saving the months in separate objects:
lapply(names(dat), function(month) {
  save(dat[[month]], file = sprintf("%s.rda", month)
 })
or using the good old for loop:
for(month in names(dat)) {
  save(dat[[month]], file = sprintf("%s.rda", month)
}