Sorry for the delayed reply, Steve!
It’s not possible currently to hide out of stock products, however this is something that’s been talked about a few times before with others. The “problem” with this feature is that it’s great if someone is browsing for something to buy without a specific product in mind, but if someone is specifically looking for a particular product, it can be unhelpful to hide it.
For example, if a customer of yours comes to your trade store looking for Super Tasty Beer and searches for it but nothing comes up, they’ll question their spelling, start clicking through categories and may eventually get frustrated as they can’t find what they’re looking for (and even think the website isn’t working properly). This might result in a phone call to your sales team where they explain the item is just temporarily out of stock, which is inconvenient for you and annoying for them.
If this item was shown (as happens now), they’ll see it and instantly realise it’s out of stock and in many ways this is a better experience for your customer.
A filter for in/out of stock items might be the best way forward as this way your customer will find the item when looking for it specifically, but can also filter out the out of stock items to make it easier for them to find an alternative. If this would be helpful for you, could you request it in the Feature Requests area and then others can vote it up the priority list? 
With the launch of both Beer/Product Tags (mentioned above) and the recent changes for filtering, you do now have far greater control over how products are shown and your customers can easily filter the exact container types that they’d like shown, rather than just all “kegs”.