conditional formatting: multiple conditions with min

Hello,

I am using Excel 2007 and I am having an issue with conditional
formatting. I have 2 columns of data that I'm working with: Column "c"
which contains both names and some empty cells, and column "i" which
contains dates and some empty cells. If there's a name in column c
then there is definitely a corresponding date in the same row in
column i. However, there are sometimes blank cells in column c dates
that have dates in column i and some rows that have blanks in both c
and i. See the following example: (I apologize in advance if the
formatting is lost when I post this message)

Sue --- 10/1/2010
___ --- 10/1/2010
Joe --- 10/23/2010
___ --- _____
Bob --- 10/2/2010

I'm using the formula below as a conditional formatting rule to
highlight the rows where the date in column "i" is the minimum among
rows that have a name in column "c":

=$I4=MIN(IF($C$4:$C$50<>"", $I$4:$I$50))

It seems to work fine when I first enter the formula. However, if I
close and reopen my workbook, then the conditional formatting
highlights the wrong cells - it instead highlights only the cells in
row c that are blank (like the 4th row in my example above).
Strangely, if I then go to my conditional formatting rule, open it for
editing, then don't change anything but just click "ok" and "apply"
then the rule starts working again, the way I intended.

Since the formula works perfectly at times, I'm having trouble
determining if it is the cause or whether I have a wrong setting or
I'm encountering a bug. Can anyone please suggest a solution or
alternate way of approaching this task?

Thanks,

~Chris