code P0171 bank lean

Hi everyone. I love my 1.2 htp 2008 but being driven up wall by the engine management light and various attempts to address the issue. The garage has replaced the lambeda? sensor, the mass airflow sensor and another sensor. The eml would remain off for a few days and then come on seemingly randomly. The fuel filter was changed and the eml stayed off for a few weeks, but back on again now. One garage said they had heard of a lazy cat converter being the route of the problem. I took it to a specialist vw/skoda garage (not main dealer) who did a smoke vacuum test with no issues.

It does sometimes seem a tad hesitant to start when cold- needs to be turned over 2 or 2 x. Had a new battery a few months ago.

I want to keep the car but not keen on idea of spending a load more money on it. 

Any ideas? Thanks lots Dawn