can anyone help me with this?

ive just been at the fuel station after getting my car out,had a very steady drive there due to 2flat tyres,left the car running while pumping the tyres up,and the radio went off and all the lights went dim,so i proceeded to batter it home so i didnt have to leave it in fuel stsion,as soon as i put me toe in,the radio came back on and the lights went back up to full power.

i had a wire off the back of the alternator a few weeks ago that caused it to die on me,i cant see now its too dark but i presume this wire is coming off again,i.e a bad connection so wen i put me foot down it sent enough current down to power everything up again?

can i replace this wire or shall i just tighten it up with grips? im pretty sure its a spade connection,its never done it before just the past two times ive had car out,so is their a underlying problem?

cheers for any help