It didn't help Sega that at one time I think they were trying to support 5 or 6 different systems at the same time: Saturn, Genesis, Sega CD, Sega 32x, Game Gear, even Master System in some regions (like Brazil). Some people think Sega made the wrong decision to shift their resources from Genesis to Saturn in 1995 since the Saturn and PlayStation combined only made up like 15% (or around that) of total sales that year and the SNES and Genesis made up most of that years sales.
The Dreamcast did start great, it had one of the most successful launches of any system up to that point. It was just that in 2000 the sales dropped off and never recovered. As it has already been mentioned, Sega didn't have the money to stay afloat with a system that kept losing money. They already had a debt of hundreds of millions of dollars, so going third party was really their only chance to stay in business.
Stratos, I think even Microsoft may have a limit. If the Xbox division started causing the company itself to lose money (while the Xbox division lost a lot of money, Microsoft as a whole was still profitable), they may consider other options. If Sony had had a second straight year of losses due to PS3/PSP, they may have chosen to drop one.