"The Lorelei Signal" is part of the 1st season of TAS and therfore of the year 2268. In the Taurean region of space are disappearing ships every 27.346 year.

Therfore a ship must have disappered in the year 2239 or 2240.
Before that it has happened 2212 or 2213.
The event before would be 2184 or even better 2185.
One ship could have disappeared there 2157 or 2158.
And it also happened 2130 or 2131.
And there was problems in that region 2102 or even better 2103.

That goes back "150 years" in the opinion of Kirk. But to be exact they are 164 or maybe 165 years.