ILS Approach Question

[meierzwo]

I do not often a ILS Approach but often, the fist Attempt did not work. The Second one is a success.

Flight Plan is set (Airways, no GPS),  following the ATC Instructions for Waypoints, Altitude, AP is in HDG and ALT Mode, LOC Freq is set, CDI is set to VNAV, LOC-ID is captured.
On the last ATC Call - Report on Localizer- I switch the AP to Approach. Both CAP Lights go Green, Plane follows the Glide Path but instead of Lining Up to the Runway for the last 3 or 5 Degrees, it goes 90 Degrees of to the Right or Left and stays on that Course. But still tries to follow the Glide Path until the Localizer is lost.
ATC cancels my Approach and sent me back into Pattern for a second Try. Flying the same Route, doing the same Things at the same Time and this Time, the ILS Approach was a success.

I had this with two Airports now. One was a uncontrolled one (no Tower or Approach Freq - Unicom - but with ILS) and I was lined up with the Runway on the Path. View was blocked from some Clouds so i switched to APR Mode. And off it goes. CAP Lights green. The second try on this Airfield did work as expected.

Second one was with a controlled Airport. ATC guided.
What causes the Plane to go 90 Degrees off Course with both Cap Lights green? And working Glide Path. I want to understand what happens here because the second Attempt with no difference in Actions did work.