Firefox always prompts to remember passwords for most of the sites.But if you deal with banking or some official restricted sites or even Yahoo Mail then you have seen that no such prompt message pop up.

Here is an easy trick to make Firefox remember these passwords.Whenever you login on that particular website and fill username and password , type the following code in the address bar of that page and press enter.You will be prompted with a message.To remember that information click “Ok”.

javascript:(function(){var ca,cea,cs,df,dfe,i,j,x,y;function n(i,what){return i+” “+what+((i==1)?”":”s”)}ca=cea=cs=0;df=document.forms;for(i=0;i<df.length;++i){x=df[i];dfe=x.elements;if(x.onsubmit){x.onsubmit=”";++cs;}if(x.attributes[”autocomplete”]){x.attributes[”autocomplete”].value=”on”;++ca;}for(j=0;j<dfe.length;++j){y=dfe[j];if(y.attributes[”autocomplete”]){y.attributes[”autocomplete”].value=”on”;++cea;}}}alert(”Removed autocomplete=off from “+n(ca,”form”)+” and from “+n(cea,”form element”)+”, and removed onsubmit from “+n(cs,”form”)+”. After you type your password and submit the form, the browser will offer to remember your password.”)})();

Alternatively
Drag and drop bookmarking icon from Squarefree.com on your firefox interface and click on that bookmark after typing password on that particular website.
P.S.: But if you are using public computer then make sure to not use this technique.