You know, that's an interesting question. It's not listed as an "official" side effect of Effexor, but there are message boards out there of people complaining of the same thing, so anything is possible.
That said, I have several ideas that you might want to consider:
1) Combination therapy can be done with SSRIs (Paxil, Prozac, & Celexa are examples) and SNRIs (Effexor, Celexa, etc) - however, it can also be done with SSRIs and a mood stabilizer like Depakote. So, if you notice too many side effects from the SNRIs, you could ask your physician about adding a mood stabilizer instead.
2) Going at the depression nutritionally isn't a bad idea. It's not a substitute for proper meds, but enhancing your diet can't hurt. B vitamins in particular increase energy. For people with depression, this is sometimes helpful. SNRIs impart some energy too, which is (in part) how they differ from SSRIs.
3) Taking supplements to improve brain health for better memory isn't a bad idea either. Some vitamins to consider: folic acid, magnesium, selenium, calcium, and fish oil.
Please remember that there are many other things (aside from SNRIs) that can interfere with memory. There is always the normal age-related decline. Depression can affect memory and chronic pain can too. Hormones affect memory and mood - when women go through menopause there are a lot of issues related to memory and retention if the hormones are out of whack. Finally, hypothyroidism can affect mood and memory as well - so the culprit may lie in one of those issues as well.