How long before my H1B visa ends should I apply for EB-2 green card category?

You cannot apply for a green card. If your employer wishes to continue your employment beyond the second 3-year period for a green card, the employer can sponsor your petition for a green card. However, so many H1-b holders have left the sponsoring employer the minute they get the green card, leaving the employer on the hook for the sponsorship support obligations, that very, very few employers will now sponsor any temporary employee-visa holder for any green card. Don't count on your employer ever sponsoring you for a green card. It is extremely unlikely.

Your permission to work in the US is temporary, and can be terminated at any time, even if the maximum allotment for the employment visa has not been used up. Your employment visa is automatically revoked as of the last day worked, and you are required to leave the US immediately in such a situtation. There is no grace period if employment is terminated or if an employment visa expires. Given the high rate of unemployment in the US (now over 23%), and mass layoffs at so many companies, make sure you always have sufficient funds for your transportation back to your country as you could well lose your job in this economic climate.