If you are booked in a category H cabin with a cabin number there is no reason for you to expect an upgrade of any kind nor would I anticipate any would be forthcoming other than some highly unique circumstance. Approaching RSSC will result in "if you wish to upgrade we would be happy to accommodate and the extra charge is $XXx."

You get what you pay for and if you pay for a category H and get a cabin number then that is where you will be.

Complimentary upgrades happen for these reasons only:
1. RSSC need your particular cabin for some reason
2. RSSC offers a general upgrade offer to everyone
3. RSSC offers an upgrade to you because of a problem you have encountered as a goodwill gesture.
4. You are booked in a guarantee (like Richard above) and there are no cabins in the guarantee category you purchased. They have no choice but to upgrade you. However, most of the time the "upgrade" will be to a higher category in a less desirable location and that is why it is still available. That is the situation with all the upgrades mentioned on this thread. These used to be great but now they are being assigned differently and there will be fewer stories like you are reading on this thread.
5. You are a VIP and therefore get upgraded.
6. On rare occassions someone will be upgraded and you have no idea why. If you happen to be one of those people take it and rejoice. You were VERY lucky.

YOu pay for a cabin category, you get a number and then most of the time that is where you stay.