Normally sugar will reactivate a live beer even a year after it has been made. However it does not need much sugar, but is a sealed container be it a bottle or a keg it should not go flat, and it would seem you have a leak, depending on what has gone into the beer it will alter the retention of a head, sugar will produce a head, but unless there are some non fermentables in the beer it will not hold the head. Kits which require sugar to be added are not as good at holding a head as kits using dried malt extract, or other two cans of wort.
The limit to adding more sugar is the point where yeast dies, with high alcohol brews one often adds the sugar in stages, so as not to stress the yeast, one can push fermentation up to around 21% with some yeasts, but the result made that way is undrinkable until one cleans it up, which removes both the good and bad tastes so once cleaned you have to then add a taste, with a kit beer designed to have 1 kg of sugar one can add up to an extra 1 kg but in doing so it gets a bitter after taste so in real terms just not worth doing. To raise the ABV better to add less water.
The o.g. or original gravity will be 1.0xx for example 1.056 you then at the end get a f.g. final gravity which will be around the 1.010 mark. Those reading would give you around 6% ABV (Alcohol by volume) I use a java script program to work it out, so can't remember the formula. The more fermentables used the lower the final reading, the more non fermentables used the higher the final reading. Using just sugar and yeast food the f.g. can go below unity, but this should never happen with a beer.
There are times where you do need to re-pitch yeast, I don't think you need to do that, but when you do, first you need to rack off the brew into a clean fermentor as when yeast stalls it sends signals out to rest of the yeast to go into hibernation, so you need to remove as much as you can of the inactive yeast before adding more. Also you need to re-pitch with a large quantity to ensure it keeps going. Yeast can stall often due to wrong temperature, and first thing is to correct the temperature and see if it restarts before racking and re-pitching.
You don't say what beer you are making, so the reply is also vague. I use all kits, so if a all grain beer I would normally leave it to others to answer. If you have problems retaining the pressure, then consider drinking as a shandy, i.e. add lemonade. Then look to find the cause and correct for next batch. I don't use a keg, I use pop bottles, in the main problem with a keg is you need so many to have a supply of different brews all which have been given time to condition. My shed will normally have around 200 pints in it, I am drinking beer started in November 2015 at the moment. I would need a lot of kegs to do that.
P.S. Writing an caps is considered as shouting, we do not use caps with normal writing.
