subset drops S3 classes?

Hi all --- I've stumbled upon some pretty annoying behavior, and I'm
curious how others may have gotten around it.
When using subset(...) on a data frame that contains a custom S3
field, the class is dropped in the result:

MyClass <- function(x) structure(x, class = "MyClass")

df <- data.frame(x = 1:10, y = 10:1)
df$x <- MyClass(df$x)
str(df)

'data.frame':   10 obs. of  2 variables:
  $ x:Class 'MyClass'  int [1:10] 1 2 3 4 5 6 7 8 9 10
  $ y: int  10 9 8 7 6 5 4 3 2 1

str(subset(df, x %% 2 == 0))

'data.frame':   5 obs. of  2 variables:
  $ x: int  2 4 6 8 10
  $ y: int  9 7 5 3 1

And so, any generic functions hooked to MyClass suddenly don't work on
the subset results, but do work on the original data frame.
I think I could write a custom as.data.frame.MyClass for all such
classes, but this is annoying, indeed (and I don't know for sure if
that's a robust solution)
Wrapping in I(...) doesn't work, either:

df <- data.frame(x = 1:10, y = 10:1)
df$x <- I(MyClass(df$x))
str(df)

'data.frame':   10 obs. of  2 variables:
  $ x:Classes 'AsIs', 'MyClass'  int [1:10] 1 2 3 4 5 6 7 8 9 10
  $ y: int  10 9 8 7 6 5 4 3 2 1

str(subset(df, x %% 2 == 0))

'data.frame':   5 obs. of  2 variables:
  $ x:Class 'AsIs'  int [1:5] 2 4 6 8 10
  $ y: int  9 7 5 3 1

(note that while 'AsIs' is kept, 'MyClass' has been removed in $x)

Cheers!

-Murat