Tannin acts as a structural component and red wines with higher tannins tend to age better than lower tannin red wines. Tannins come from contact to the pips and skins of the grapes during wine making and also from oak aging. A wine with well balanced tannins (where there is a balance between ‘grape tannin’ and ‘wood tannin’) will slowly “smooth out” over time as the tannins break down. Despite the fact that tannins can help make a wine age well, if the wine is not well balanced to begin with, it will never improve over time. There are many long-lived white wines and white wines do not need tannin to age well.
Alcohol is volatile in non-fortified wines and causes wine to turn to vinegar more quickly. Generally speaking, the lower the alcohol level in a non-fortified wine the longer it will last. There are, of course, exceptions to the rule. However this is the case for many dry red and white wines. When seeking out a wine for aging, I check the alcohol level and hope for an ABV below 13.5%. Despite the fact that high alcohol ruins normal still wines, fortified wines are perhaps the longest lived of all wines with 17-20% ABV.
This component of a wine is often overlooked because of the popularity of aging dry wines. As it turns out, the longest lived wines tend to be sweet wines including Port, Sherry, Sauternes, and Riesling.