How to Fill A Deep Driveway Crack

Depends on what's at the edge of your driveway? is it grass? then you might want to brace with a 2x4 against the ground just to keep the edge nice. If you don't want to dig up the ground to put a 2x4 in the ground you could probably get away with a thinner piece of wood.

• Option A: keep doing what you did, and expect it to fail every winter; be pleasantly surprised if it does not some years.
• Option B: tear up the driveway and put a proper base under it. The lack of a proper base is almost certainly why it self-destructs in winter.

If you can stand the annual work, Option A can be done for MANY years before you begin to touch the price of Option B.

"A proper base" will depend in part on the underlying soil (a good deal of which may need to be removed and replaced with compacted rock and gravel) but is generally a firm, well drained foundation.

If you're really independent-minded there is also Option C: tear up the surface and change to gravel/rocks rather than a hard-surface driveway - takes some annual raking, but immune to cracks for the most part.

Edit, Add: Depending both on the existing grade and soil type, you might get some benefit from digging a French drain (drain pipe under rocks) down both sides of the driveway to help keep water from going under it sideways, and help remove any water that does get into it, at less cost than the full dig up and replace the whole surface. If you have porous soils (sandy, gravelly) this will help a lot, if you have clay it will be of more limited benefit.