instead of thinking about "losing out" consider it "winning in". Whitelabel is an awesome idea. Consider you have a web app and you charge $20 per month. You have advertising costs, etc.
A whitelabel scenario would be that you charge company x a base of $10 per month. This covers your continued development costs, hosting etc. What it doesnt include is advertising, company x will have to advertise the product themself. You then allow company x to set thier own pricing within your guidelines. Say you tell them they cannot sell a subscription for less than $18 (so that it wont be much cheaper than your own product).
The customers that company x brings are customers you likely would not have had. Or customers you would have spent $$$ to get in advertising. This is a winning model because it allows company x to focus on sales alone, not having to worry about dev and hosting.
The bottom line, if you have a service that you sell, you have created a Stamp.
Think about it that way. you create an ink stamp. The work goes into the design and manufacturing of your "stamp". Each time you dip it in ink and stamp it you get paid. So your customers bring you a blank peice of paper, you stamp it (costs you pennies to do so) and you get paid!!!
with the white-label, you allow others to use your stamp, where they earn a certain percentage and you do too.
Plus think of it this way, if you gave up 50% to white label. You keep 50%. Two whitelabels and you are making what you would normally without the sales overhead. 20 white-labels and you are making 10 times what you would make on your own efforts.
Take it, build a strong relationship, and start thinking about how much money your partners are making you, rather than how much your partners are costing you.
Last, if its a web-site or service, make sure to offer custom dns subdoamins or domain names...