GPS EM-406A issue

Hi,
I am the owner of an old GPS logger shield from Adafruit that hosts a GPS module EM-406A.

I bought all this in 2009.
I've never used it very intensively, approximately once every year when I felt in the mood for an openstreetmap outing.
Last week I dusted my GPS shield for a new mission. At first glance everything went well. But after some tinkering I realized that my GPS module EM-406A was able to localize itself (blinking led) only after it is powered off for a while. For example, if the GPS is working properly and for some reason I power it off and on, it will never get a fix and the led will remain lit. To make it work again, I need to wait one hour (haven't determined precisely the time I need to wait).
Has anyone ever seen this behavior with this module or another GPS? How can we explain this?

If there is a backup battery on the module, replace it. It is probably dead or dying, which would interfere with the backup memory integrity.

Thank you very much for the explanation. It seems that the module suddenly shuts off when the power voltage goes off. Instead it should use the power from the supercap to go to sleep properly.
The datasheet says:

Built-in SuperCap to reserve system data for rapid satellite acquisition

Do you think I can fix this? Everything is built in a PCB with a soldered shield on either side.

The supercapacitors typically used on those GPSs are only good for 2-4 hours of backup, then there are flat.

A backup (of satellite data) older than that is of no use anyway, 'rapid' satellite acquisition only occurs if the saved data is relativly recent.

etimou:
To make it work again, I need to wait one hour (haven't determined precisely the time I need to wait).
Has anyone ever seen this behavior with this module or another GPS? How can we explain this?

Sounds like a dodgy antenna or similar.

A GPS from cold ought to get a fix in 45 seconds or so if its outside with a good view of the sky.

Troubleshooting steps to be found here;

GPSTutorial