Longer time between BLE advertisements
The &quot;BLE rules&quot; you refer to would be the &quot;Core Specifications&quot; of the Bluetooth Special Interest Group (Bluetooth SIG). As far as I know, they do not place a limit on how infrequently a device can advertise.
But you may run into problems connecting, if using a smartphone as your central device. Although you might guess otherwise, scanning uses almost as much instantaneous current as transmitting, and since it runs much longer than transmitting, it is a greater consumer of battery energy. As a result, the smartphone OS generally only scans for a limited period after each request. You can, of course, bypass this by repeatedly requesting a scan, but the battery life will suffer.
Focusing back on your peripheral, you should calculate a power budget to determine how much battery energy is consumed by the periodic advertising versus the baseline current draw during sleep. Even though advertising draws several mA, it only lasts a few mSec. Once the advertising interval is longer than a few seconds, you will find the sleep current, even at a few microAmperes, takes a bigger part of the energy budget than advertising.
Also, instead of advertising and scanning, consider maintaining an actual connection, with a long connection interval, and a high value for &quot;slave latency&quot; (number of connection intervals the peripheral is allowed not to respond, without breaking the connection). This tends to optimize battery life for both the peripheral and the central device.