Our shared fence is falling apart. My neighbour wants to upgrade it. Do I have to pay for any of this?

Since the fence is on the property line, you’re equal partners in its upkeep. Generally this means you have to split the cost of repairs. But there are exceptions. 

If your neighbour wants to rebuild a “fancier” fence than is necessary, you’d have to agree on how the costs should be split up. This fence is half yours, after all, and can’t be removed without you agreeing. And if you can’t agree, but your neighbour insists on the new fancier fence, then your neighbour will have to pay for the whole new fence. 

There could be other factors in play here. For example, if an upgraded fence is functionally necessary, which might be the case for a retaining wall, then you may have to split the costs.

To preserve a good relationship with your neighbour, you could offer to pay for part of the new fence they want to build. (Perhaps you could kick in half of what it would have cost to fix the old fence.) In the future, you’ll probably have to split the repair costs evenly (if the fence is on the property line), so long as the repairs are reasonable.

You may find this coverage of fences and neighbours helpful. In particular, see the section on how to work out problems.