The print permanence achieved by selenium toning is in direct proportion to the degree of toning. Unless you plan to tone to completion, which usually means a very, very reddish-brown print tone, you're likely not getting much protection. All the buzz about selenium toning to help preserve prints is based on a study done on microfilm stocks. Toning the microfilm to completion gave significant protection. People then tried to apply that to prints and, somehow, the urban myth arose about toning slightly in selenium to provide extra permanence. I simply doesn't work that way.
Really, if you choose to selenium tone, you should be doing it for the change in tone you get, not to try and somehow make the print more permanent. If you want prints with great longevity, take care in processing. Most important here is not exceeding the fixer capacity and washing the prints well.
As for the your toning solution turning brown: I never have that problem. I use Kodak Rapid Selenium Toner (with fiber-base paper) and transfer prints directly from the second fixing to the toning bath. After a toning session, I filter the toner through a regular paper coffee filter and save it. Before the next toning session, I filter it again. When toning times get too long, I simply add a bit of concentrate to replenish the solution and bring activity back to a comfortable level. I have solutions of toner that are more than ten years old still going strong, no discoloration at all except for the black precipitate that needs to be filtered out before and after each session. You may be contaminating the toning solution somehow or, maybe, your fixer is exhausted and you are transferring too many waste product compounds to the toner along with the print. Does the discoloration happen when using fresh fix? If so, it may be something in the Berg toner that's not in the Kodak product.
I really hate to simply contradict other posters here on the forum, but I feel that the record really needs to be set straight. So...
-You do not need to rinse well between fix and toning. Ansel Adams didn't and I don't. I've been transferring prints directly form fixer to toner for 40 years now. Toning is fine that way; no stains, no problems provided that you use a fixer that's not too acidic like Ilford Rapid Fixer 1+9 or one of the alkaline fixers on the market. If you use Kodak powdered fixer and get stains, change fixers.
-The presence of fixer doesn't make my toner go brown at all. My prints are not rinsed at all between second fix and toner. No brown toner, no stains on the prints. There is certainly carried-over fixer in my toner, which causes a precipitate that I filter out, but otherwise, no change in toner color.
-Unless your getting a change of color or a significant change in print density, you are not getting much protection from selenium toning. Selenium binds with the silver in the emulsion; it doesn't just "coat" the print with something protective. That binding with the silver grains is what causes the change in tone and density. Without that, no protection. And, selenium toning is nothing like treating the print in Sistan or other similar protectants.
-And, FWIW, a properly-fixed print should not have any silver halides left in the emulsion. If there are any, it is a sign of improper fixation. The image-forming silver is pure metallic silver. Silver halides that don't get developed need to be removed by fixing and washing.
Hope this helps,
Doremus