Photoshop :: Converting Images To SRGB For Web

I'm having a bizarre, when I try to convert any color profile from Adobe RBG to sRBG to ensure better viewing colors on the web. I actually go through the process twice to confirm that I've done it -- I convert the image's color profile to sRBG under the "Edit" drop-down menu, then I double check to make sure that sRGB is selected when I go through the "Save for Web" option under the "File" drop-down menu. The converted images still look muddy when posted online, and it always puzzled me why when I open them up again in PS, it tells me that the image has no Color Profile, and I need to assign it one. I would just ignore the message, thinking it didn't apply because I had already done it twice previously. The other day, I opened up one of my twice-converted sRGB images and when prompted, assigned the profile to sRBG a THIRD time. Finally the image came out perfectly on the web. Now whenever I make that third sRGB conversion on web images, the profile remains permanent. This just makes no sense to me. I should only have to convert the profile once.