Wine does improve in many ways as it ages, but it doesn’t get drier. So depending on what kit you got, it could take anywhere from 3 months to 2 years to hit it’s peak and the grape flavor might fade, but it will still stay sweet.
To avoid this happening in the future, you have to understand why it happened this time. Two possibilities come to mind.
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You bought a kit that is optimized to make a sweet wine. Kit makers cater to all tastes and enthusiasm levels, and you need to pick out the kit which is geared towards your needs. Read the labels to see if it explicitly states it makes a dry wine. In general, the more expensive the kit is, the better the wine will be. Similarly, the longer the kit says it will take to complete, the better the finished wine will usually be.
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The yeast didn’t finish fermenting completely because the conditions weren’t right. Kits tell you to take a step-by-step approach based on how many days between steps. Usually, that works OK, but not always. Sometimes, for whatever reason, a certain step needs more time, and if you don’t give it that time, you don’t get what you were expecting. So if you fermented in a room that was colder than the kit maker expected, or you didn’t oxygenate the must as vigorously as you should have, or the yeast was old or whatever, the fermentation could take longer. If you then added your sulfite and sorbate on the kit schedule, you stopped the fermentation from completing and left too much unconsumed sugar in the wine.
If the second situation was the cause of your problem, then there are a number of steps you can take to fix it. First, realize that you can mess up by rushing things, but you will almost never cause problems by waiting. So if in doubt, give it more time.
Second, don’t stop the fermentation on a time schedule, but instead use a hydrometer to confirm the wine is fully fermented before you stabilize. Dry wines will typically go down to a range of 0.992 - 0.995, though exactly how low depends on the yeast strain.
Use a yeast strain that attenuates more. This is what the brewmaster you spoke with recommended, though if you are buying kits, it is probably best to stick with the yeast they provide. But after you get more experienced, you might want to experiment with different yeast strains. Some, like Lalvin R2 leave some residual sugar when they finish. Others, like EC-1118 ferment very dry. The specific strain is more important than how much you use. Generally, one 5 g foil package or a single liquid pack is enough for a 6 gallon wine kit. Be aware though that the yeast strain has a big influence on not just the residual sugar, but what flavors are going to be generated in the fermentation. So read up on the topic before changing what the kit maker gives you.
There is one trick that is often used with white wines to push the yeast to finish drier. When the fermentation has progressed about 3/4 of the way (specific gravity has dropped to a range of 1.025 - 1.015), rack the wine to a new fermenter, while gently exposing it to the air. “Gently” is important here, you don’t want to splash it around a lot and put too much O2 into it. The preferred method would be to position the end of your siphon hose near the top of the clean carboy or bucket, and let the wine flow down the side of the container in a thin sheet that fans out. It is important that you don’t do this too late (SG < 1.015), otherwise the yeast won’t have enough food available to consume the O2 that will get introduced, and you could end up with stale tasting wine.
Good luck.