Type II errors are invisible, which is why they get ignored. You never see the equity curve of the system you threw away. But they are common in trading research because edges are small relative to noise and samples are short.
The probability of avoiding one is statistical-power. A system with a true expected return of 0.05% per trade and a 1.2% standard deviation needs roughly 4,000 trades for an 80% chance of detecting it at the 5% level. Most retail research has 200 trades and therefore almost no power.
The useful response is not to loosen your threshold, which just converts type II errors into type I errors. It is to test on more instruments, longer history, or with a design that uses every observation, and to accept that some real edges will remain unprovable at your data budget.
Related: type-i-error, statistical-power, sample-size, signal-to-noise