I'm about to add oak to my second beer, having thrown out the cubes from my first tasty experiment. This time I hope to pull them back out, store them in bourbon, and re-use them.
How much of the oak flavor is lost with each re-use?
It depends on how long you leave them in the beer. Manufacturers of various oak products - cubes, beans, staves, chips, spirals, powder - sometimes mention how long it takes for them to give up everything they have. The lower the surface-to-mass ratio is for your cut of wood, the longer they'll last. I.e., staves last longer than cubes last longer than chips last longer than powder. I believe 3/4" cubes are good for about 4-6 weeks of contact time. After that, they're spent. YMMV, but if you're only leaving them in the first beer for a week or two, they definitely can be reused. The second time you use them, it will take longer for the beer to extract the same amount of oakiness as it did the first time.
Note that if you store them in bourbon, the bourbon will extract oakiness from them, so you will want to add that liquor to the brew, too.
With things like cubes and chips, I've found that it's best to just throw them into your BBQ right before you put the meat on after they've been used in your beer. If you think about it, you've conditioned them with wine or bourbon prior to use in your beer. There's not a lot of surface area there, so they're probably mostly spent by the time they've rested in your beer for an additional month or so. They're inexpensive and you can buy them in bulk from places that sell adjuncts to wineries, like xtraoak.com , so why not start fresh each time. You want the best possible beer, right? Right.
Barrels can be re-used quite often, depending on the style of beer you're brewing. For example, I turn French Oak barrels that I've used for Chardonnay and Pinot into secondary fermentors for my IPAs, and those can be re-used several times. I haven't hit the end of the line with any yet, though you might want to supplement with staves on older barrels-- use your nose and tastebuds to determine that one. If you want an lot of oak influence in your beer, then you want to go with a newer barrel. But keep in mind what was in it before-- a bourbon barrel that held bourbon for a year will extract more tannin from the oak than a 14% chardonnay over the same period. One thing I've found is that really new barrels are overpowering for most beers, unless you just want smokey oak notes throughout. It can come across as skunky or just off.
You can reuse them several times, but each time you will need to wait longer to get the desired effect. Consider that Rodenbach brewery disassembles their oak vats between batches and scrapes some wood off them. You have the benefit of being able to taste the effect and remove the beer from the oak when you've reached the level of oakiness you want. You can even sanitize and add more fresh oak if the reused oak is taking too long.
However, I would say that the difficulty in storing the oak in a sanitary way between batches and sanitizing the now sugar- and yeast-impregnated oak outweigh the cost of just starting with fresh oak each time.
The only oak I reuse in my home brewery is my 20 gallon oak cask.