The chart clearly traded through my limit, but the trade did not execute, why does this happen?

It is possible for the market to trade through a limit without your limit order being executed. This occurs when there is not enough liquidity available to fill all orders at the price points displayed on a chart. Generally speaking, this is more likely to occur during news announcements when liquidity tends to be low.

Imagine that over 20M sell limit orders are sitting on a brokerage platform at the price of 1.3350, while the market is at 1.3320. A news announcement comes out that spikes the market from 1.3320 to 1.3355 within a few milliseconds. You watch this occur on the chart and subsequently watch the market drop back below your limit within seconds. The tick chart clearly traded through your limit, so why were you not filled?

Generally, a spike like this occurs as one liquidity provider makes an aggressive bid to the market. Due to the risk involved, the liquidity provider will normally quote a small amount, say 1M. If 20M worth of orders are sitting in the market, then only 1M can be filled as the price spike had only 1M attached to it. As such, the remaining 19M worth of orders are simply reset, awaiting the price to touch that level again. Note, generally speaking, price spikes on tick charts reflect limited liquidity amounts.