How about over time, as you use the enchanted weapon, the enchantment slowly becomes less and less powerful until it dissipates entirely and you have to re-enchant it with whatever enchantments you want? It would still last for a long time - I'm not talking 20 swings and then it's gone, like Oblivion.
The stronger the enchantment, the longer it lasts, since it would be a linear rate of decay - i.e. imagine a Weakness to Frost 100% enchantment vs. a Weakness to Frost 40% enchantment which both decay at .1% per swing. This means 400 swings before the 40% is gone, while the more powerful 100% lasts for 1000 swings. Then, you just re-enchant.
Obviously, the rate of enchantment could be tweaked for specific weapons, or you could make some enchantments not decay at all. You could also just vary the decay rate of weapons in general instead of only changing it for specific weapons - for instance, generic named enchanted items (i.e. War Axe of Numbing) would decay quickly while unique artifacts and weapons would decay much more slowly. This would keep the player from losing special/rare/unique enchantments quickly. You could also keep them from completely disappearing off of those unique weapons or you could cap the decay at a certain point - with either of those two systems, "re-enchanting" it would just recharge it. Maybe those weapons don't decay at all. I don't really know.
This also has the added bonus of being able to add more powerful enchantments to a weapon as the older ones wear off, and I say "added bonus" because I think it would be cool to be able to keep the same weapon for a long time and upgrade its enchantments over time. It would make it feel more like the weapon belongs to you, instead of just being some generic steel sword you found. After all, most heroes have their own unique weapon to their name (Arthur had Excalibur, Aragorn had Anduril, etc...). So potentially, a steel sword you grab at level 3 or 4 could be one you use for the next 20 levels that you are constantly making more powerful (this would also work really well in tandem with Skyrim's new blacksmithing system if there is a way to upgrade the physical damage or look of a weapon - don't know if that's at all what it's going to be like though). Some sort of weapon progression like this would be really neat IMO.
Just an idle thought I had while playing some Oblivion. Wondering what you guys, especially people who hate the current soul gem/recharge system, would think about something like this in Skyrim or another future TES game. I got a little off-topic with the weapon progression idea; mostly looking for feedback specifically on the enchantment aspect and how you guys think it could work.