It highly depends on the environment where you keep your safety razor. If its left open in the bathroom, then yes, 2-3 days only. If inside a cupboard, away from moisture, you can go beyond a week.
For example if I would shave once a week and decided to let the razor in the bathroom, should I replace the blade after each use?
No. Just dip the razor head in mineral oil before you put it up for the week. On the other hand, blades are about 10¢ each. I have about ten razors in rotation at any given time. I keep them in the bathroom, and I don't change the blades in any of them until they get dull. That might mean a blade stays in a razor for a month or more, depending on how often it gets used. I've never had any issues. My normal routine is to rinse the razor, dip it in barbacide for a couple minutes, rinse it again, dry the blade and razor, reassemble it with the blade and store it.
Like Ryan said, blades don't cost that much. I did the rinse then barbacide and rinse thing as well when I had multiple razors in the bathroom. When I take the razor out of the bathroom and too a dryer environment, I don't worry about how long the blade lasts. However, then I have to keep track of how shaves were on the blade. It is simple enough to test, if it shaves well a week later, then it didn't damage the blade. However, I would still use the barbacide or a similar treatment to make sure you don't have a teaming ecosystem in there.
Think about it this way. If a blade is 0.10 each really (0.04-0.10) and you use a new blade every week that's $5.00 a year on blades. Why not shave with a new blade every week? It seems like a lot of work cleaning, rinsing, cleaning plus stuff on the counter to save yourself a few bucks.
I use one razor (Gillette Canadian Heavy Tech...a real peach)...I change my blade every Sunday morning and get a week's worth of shaves from it. I also give my razor a cleaning when I change the blade. No worries about rust. I do occasionally shave with another razor...but I always remove the blade when I am done and make sure everything is dry before I store it in my box of razors.
My blade goes in fresh on Monday, goes into a different razor every day, gets hand stropped before every shave, and gets tossed after Friday's shave. That's 5 days in a razor that stays hung on the wall in the bathroom. (I have a rack that holds 21 DEs and 9 SEs) So to answer your question, 5 is obviously more than 2-3 days. My wife shaves her legs once a week with her Pink Lady Gillette. The blade stays in her razor, in the same bathroom, for 4-5 weeks. I clean her razor for her after every shave (take blade out, rinse and dry the razor, hand strop the blade and return to the razor) and I have not seen any problem. Her 4-5 shaves per blade are exactly what I, and many others here, get.
my razor rotation? is very loose. I tend to use whatever razor I have a whim for. I don't keep blades in each razor. I use one blade until it's used. after I shave,I mostly remove the blades, dry it. leave it inthe bathroom until tomorrow. sometimes it's left in the razor, but mostly removed. I get about for shaves per blade.
The edge is exposed and is drying so fast that it does not matter much how long time you keep the blade in the razor. I am rotating some razors according to mood. Sometimes there is a long break (a couple of weeks) before I return to an earlier loaded and used razor. This has never been a problem.
I rotate my razors in no particular order and only use a Feather blade. I never keep a blade in a razor and it only gets used 2 times. YMMV
Great question! I was given my wife's Grandfathers Gillette Super Adjustable 109 (black beauty) last year. He passed 25+ years ago, when I got the razor it had a used blade in it. No sign of rust or corrosion. The razor/blade were still good to go.
Do you mind posting a pic of your razor rack? Figured I better specify or who knows what kind of picture I might get! As to the original question, I would assume they could last a while. You might want to disinfect them if you let them sit for a very long time (or just swap it out). Similar to @RaZorBurn123 and his experience, I found a Gillette SS at the flea market that had a blade still in it from who knows when. I asked the guy about the blade and he said it had been in there since he got the razor a few months before and he did not know how to take it out. I opened it and took out the blade and there was absolutely no rust or any issues with the razor or blade and it had been sitting out in South Carolina humidity all summer.