The difficulty is in how you are thinking about the problem. You are thinking of capital gains as income and that is not intrinsically true. Consider a person who purchased a home in 1970 for \$14,000. They sell it today for \$150,000. That is a capital gain. However, if the cost of goods has gone from \$14 to \$150, then the sale is neutral. They have exactly the same amount of money as they started with. Particularly for those living in poverty, their capital gains are real losses and not real gains.
If you live in poverty then you cannot maintain or provide general upkeep. This causes a deterioration in the assets and so they lose real value even if there is a nominal capital gain.
Poverty is also about daily living and not single transactions. Although some impoverished individuals do have capital assets, this is a trivial percentage of that group. Most of them are retirees who are gradually spending down everything they own. They may have incidentally purchased 100 shares of AT&T fifty years ago and never sold it. In that case, when it is sold it is a real gain, but they cannot live off of it until it is sold. You are impoverished even if you hold assets you could sell.
For example, the median net wealth for Caucasian women, aged 35-45, is slightly less than \$42,000, but for women of color of the same age, it is \$50. This difference is due to being more likely than Caucasian women to be laid off and to be laid off for longer periods of time and due to receiving lower wages. You have to spend down assets when you are unemployed and you may not be able to save if your wages are sufficiently lower. That number is a net wealth. Some of those women own capital assets, such as for retirement, but they have offsetting debt. The debt is not considered either in poverty calculations.
Capital gains are not included because they would require an exceedingly costly, per person, analysis of the circumstances to determine if it was a real gain or a nominal gain. Remember, if a person moved from or to a high-cost area the value of the gain could be completely different. The same is true if they moved from or to a low-cost area. A \$5,000 gain in New York City or Anchorage Alaska is negligible, but it is material in West Virginia or Mississippi.
Captial gains are also excluded because the percentage having capital gains are quite small. Capital assets are not commonly an element of the portfolio of the poor. Half of all Americans do not have bank accounts, let alone stocks. Most of the poor carry all of their assets with them all of the time. Indeed, one way to materially alleviate poverty is to engage in acts that compel banks to move branches into poor areas. The presence of a bank makes it safer to open businesses and triggers lending, which in turn triggers more businesses and an increase in wages. Banks are highly resistant to move to areas where the business does not already exist, hence the Community Reinvestment Act which compels banks to at least reinvest some assets in the communities that they serve in even if they are not yet high-profit locales.
It would cost a small fortune to collect and calculate the data and it would be to measure a small effect.