I enchanted my sword with Absorb Health and Fire Damage, with relatively high charges and a Grand Soul Gem. But after a few swings, it has already lost it's charge. I've read that dual enchanting a weapon makes it have a smaller charge, so I'm wondering if it's really worth it to dual enchant a weapon, or, if there's a way around it.
When you dual enchant a weapon, each swing will trigger both its enchantments and both will drain its power. This is why your weapon lasts half as long. Overall, you get the same amount of effect out of it- it's just focussed into fewer swings. It's the same tradeoff you make when you choose how much extra damage you add per swing.
To stop your weapon from burning out twice as fast, make each enchantment half as powerful per swing and you'll get the same number of total swings.
Alternatively, accept that you have a very powerful weapon that needs a lot of souls and make sure you have plenty of souls for it. Making Soul Trap one of your enchantments and carrying Azura's Star is an effective way of doing this.
You can reduce how much charge is used by using the correct Fortify spell school. It is determined by the color of the weapon.
In your case, since both effects are destruction, you will want to get some fortify destruction to lower the charge use.
At fortify 100%, your weapon will not use any charges.