I had exactly the same issue when I bought my Intensity Pro PCI Express card in February to transfer VHS tapes, bursts of black frames and strobing from picture to black, and the sound slowly going further out of sync as I transferred. The condition of the tape made a difference, a home recorded tape strobed much more than a retail tape. Anyway after a post on here, someone said I'd needed a Time Base Corrector.
I had no idea what a TBC was, but after reading up online, and waiting a month or so for one to come up on eBay, I opted for a DataVideo TBC-1000 for £160 buy-it-now. Time Base Correctors can be really hit and miss quality-wise, and it's not even like you get what you pay for since they're all expensive, even the crappy ones. I borrowed a fairly new CYP CTB-100G Multi-System Time Base Corrector from a friend just to test out that not having a TBC was the issue, and the quality difference between the two TBCs is massive. The CYP was more expensive than my TBC-1000 unit the quality on mine is so much better. There is a good guide to TBC buying on the digitalfaq forum, I can't post the URL, but if you google "digitalfaq time base corrector guide", it's the first thing that comes up
I have used to use an Asus My Cinema ES2-750 Hybrid PCI-E TV Tuner Card to capture, and that never gave me any issues with black frames, but it also only captured a 25fps analogue PAL signal. The Intensity card captures both PAL and NTSC, even PAL-60 (although the colours are not as accurate when played with a fully NTSC VCR). I think it's down to the Intensity pro card expecting a very exact signal, and between the older VCR and older tape, the fine sync isn't 100% perfect and a TBC fixes that, but someone may correct me on that.

My current setup is a UK PAL JVC HR-S7600 S-VHS VCR (for PAL tapes) and a US NTSC JVC HR-S9500U S-VHS VCR (powered by a Goldsource ST-1500 1500w 240v/110v voltage converter, for NTSC tapes), through a DataVideo TBC-1000 Time Base Corrector using S-Video cables, to a PC with an Intensity Pro PCIe Capture Card. This rig allows capture of both NTSC & PAL S-VHS/VHS tapes, and has transferred NTSC & PAL BetaCam, BetaCamSP & Digibeta tapes in the past (matching players & TBC/Genlock units were borrowed through a friend).