From the Philips 80C51 Family Hardware Description:

"The External Interrupts INT0 and INT1 can each be either
level-activated or transition-activated, depending on bits IT0 and IT1
in Register TCON. The flags that actually generate these interrupts
are bits IE0 and IE1 in TCON. When an external interrupt is
generated, the flag that generated it is cleared by the hardware
when the service routine is vectored to only if the interrupt was
transition-activated. If the interrupt was level-activated, then the
external requesting source is what controls the request flag, rather
than the on-chip hardware."

Should you be using the edge-triggered mode?

You can download the 3 documents in the 80C51_FAM_*.pdf series (and loads of other useful info) from:
http://www.semiconductors.philips.com/products/all_other.html