lm() with many responses

I have one array of predictors, one observation per row, and one array of 
responses, also arranged one observation per row.  I arrange these into a 
data.frame and call lm() with a pasted-together formula.

I would like to call lm() with a number of responses in excess of 100, but 
for some reason, 39 seems to be a limit.  Why do I get an "invalid variable 
names" error from model.frame() when supplying 40 or more responses?

As a workaround, I can loop through groups of 39 responses in separate 
calls to lm(), but that seems inefficient and possibly version- or 
platform-dependent.

Here is my best effort at a minimal example showing the problem.

--- begin pasted R session ---

test.this <- function(n.resp, n.obs, n.pred) {

+ my.resp <- matrix(runif(n.resp * n.obs), nrow=n.obs)
+ my.resp.names <- paste("Response", 1:n.resp, sep=".")
+ my.pred <- matrix(runif(n.pred * n.obs), nrow=n.obs)
+ my.pred.names <- paste("Predictor", 1:n.pred, sep=".")
+ my.formula <- as.formula(paste("cbind(",
+   paste(my.resp.names, collapse=", "), ") ~ ",
+   paste(my.pred.names, collapse=" + ")))
+ d.tmp <- cbind(my.pred, my.resp)
+ d.tmp <- as.data.frame(d.tmp)
+ names(d.tmp) <- c(my.pred.names, my.resp.names)
+ my.lm <- lm(my.formula, data=d.tmp, model=F, qr=F, x=F, y=F,
+   na.action=na.exclude)
+ my.lm
+ }

# Now, try it.  39 response vectors is OK, but 40 causes an error:
m1 <- test.this(40, 10, 2)

Error in model.frame(formula, rownames, variables, varnames, extras, 
extranames,  :
       invalid variable names

m1 <- test.this(39, 10, 2)
# No error for n.resp == 39.
# Also, shouldn't "qr=F" in the call to lm() turn off output of m1$qr?

# m1$qr exists.  I'd like to save memory and omit it if possible.
str(m1$qr)

List of 5
$ qr   : num [1:10, 1:3] -3.162  0.316  0.316  0.316  0.316 ...
 ..- attr(*, "dimnames")=List of 2
 .. ..$ : chr [1:10] "1" "2" "3" "4" ...
 .. ..$ : chr [1:3] "(Intercept)" "Predictor.1" "Predictor.2"
 ..- attr(*, "assign")= int [1:3] 0 1 2
$ qraux: num [1:3] 1.32 1.34 1.42
$ pivot: int [1:3] 1 2 3
$ tol  : num 1e-07
$ rank : int 3
- attr(*, "class")= chr "qr"

# Here's my version:
version

        _
platform i386-pc-mingw32
arch     i386
os       mingw32
system   i386, mingw32
status
major    2
minor    0.1
year     2004
month    11
day      15
language R
--- end pasted R session ---

Best regards,
John