What are some of your best arguments to show mutualists that property rights shouldn't be lost without use? If someone uses a patch of land for farming, homesteading it as his, but doesn't use it after that, can it still be considered his? When do you considered something as abandoned, and up for grabs again?
I recommend that you read (or watch) Crusoe, Morality, and Axiomatic Libertarianism. I don't think homesteading is the basic principle of libertarianism, or at least for me it is not. I think a far more fundamental aspect of libertarianism is the preference for social cooperation over social conflict. Homesteading happens to be one of the best rules for cooperation, as it is simple and easily applied to everyone equally. However, that doesn't mean that if you and I come up with a different (mutual) arrangement, that homesteading is necessarily better than that arrangement. For example, you and I might say that whoever "calls it" first gets to own the object. There is nothing inherently wrong with this arrangement, and it might be great between the two of us. But we cannot expect anyone else to necessarily agree to it. So a rule like that might work well for a group of friends or family, but first use is far better for society. It's just easier to keep track of and more people will agree it to.
Regarding abandonment, it depends upon the norms. A necessary condition of property is that the owner must claim the object as property. If I no longer claim my farm as my own, then it's no longer my farm. Of course, this might not be true in a statist system, where it may be illegal to abandon certain property. But whether or not a farm can remain someone's property forever, I don't think that there is a clear cut answer in libertarianism.
You will find some who say it remains indefinitely, but I think they have applied a poor methodology (a priori law). I think it's far better to leave the question of abandonment to private law. But put simply, if a farmer ceases to use the land for farming, as long as he hasn't rescinded his claim on the land, he has not abandoned it. As to what actions signal abandonment, I think that is best left to norms.
I wrote this quickly and I'm about to head out for the day, so hopefully I made sense.
I've mostly stopped talking with mutualists :P I'm happier now
(For any left-libs on here, yada yada about me putting my hands on my ears)
As to abandonment, to me it seems like the criterion for continued ownership of the land after homesteading drops to intended future. If you can somehow show that a person doesn't even intend to use the property in the long-run, you might be able to make a case for homesteading of abandoned property.