I have a small business card that is currently a JetBlue card (need to reset expiration on some JetBlue points!), and has in the past year been a DL card, a SimplyCash card, and a Blue card. I've done other small business conversions, and other than not being able to convert between a charge card and a credit card, have yet to run into a card not being able to be converted. (Though I am guessing that the Plum card is most likely an exception to this, despite being a credit card.)

It may be that personal cards are more limited in conversion. Also, in almost every case, when I've converted a personal card the conversion did not take place until the next billing cycle cut. The only exception was when I recently converted a Gold Rewards Plus to a Green card, which took a week or so mid-cycle. Whenever I have converted a small business card, the conversion took effect in 1 - 2 days.