Hi,
I was using a Velleman programmer with its ICSP output, I had exactly the same problem, the easiest way is to use a diode (a 1N4148 is fine) from the VPP pin of your ICSP socket to the VPP pin of the Chip.
There should also be a reverse diode via a 1K (ish) resistor up to the VDD line to prevent the VPP voltage passing to VDD.
When the ICSP line goes LOW after programming the chip, the first diode causes the VPP pin to remain at VDD via the second diode from the VDD line.
But when the ICSP pin goes to its programming voltage, (ie nominal 12/13v) the first diode 'passes' the power to the VPP pin as it is above the VDD voltage, so raising it to allow for programming and the second diode prevents this voltage getting through to the VDD supply.
Hope that helps
Roy