The power of attorney at the first instant is not valid.

The power of delegation can not be further delegated.

So either all there or two out of three by board resolution could appoint a POA holder .

here they delegated the authority t third director to appoint POA holder which is not valid.

For argument sake if the authority given to 3rd Director is held to be valid then on death the POA stands revoked or till it is revoked by other 2 directors. Resignation of 3rd director would not affect the validity of POA.

I repeat here the POA itself is not valid under the circumstances as sated above.

From the moment, director looses his directorship for whatever reason, POA expires.

POA ceases on demise of third director 

2) if third director resigns ask him to revoke the POA 

No power of attorney never cancells only on death.  It depends on for what purpose it was given the intention is fulfilled or not. 

1.  The POA executed by virtue of a BOD resolution by a third director would remain in force, till retracted by another BOD resolution.

2.  The POA lapses, on death, ONLY in case it is executed by an individual capacity (not BOD resolution).

3. For immovable property POA should be stamp duty paid (500/-) and duly registered with the local Registrar of Sub-Assurances.  ELSE the POA would be null & void and shall remain legally non-enforceable.

1. if the director dies, the POA will still bind the company

2. if the 3rd director resigns from the company, then the POA will be binding on the company, unless it is stated in the POA that it will be automatically revoked when the grantor director resigns from the company 

3. the 3rd director is only a conduit or messenger of the company since a company has to act through the agency of some person

4. the authority of the agent will come to an end when the board resolution resolving for appointing an agent for the company for its property through one of its authorised director, is itself revoked by the company by a fresh board resolution 

Yes it is a valid power of attorney as POA is appointed on behalf of company and the director also signed on behalf of the company. 

Also in second case it will be valid.

The power of attorney will be automatically cancelled upon the death of the principal.

Here the principal is the director of the company and not an individual.

He has appointed a power agent in the capacity of  a director and not in his individual capacity.

Therefore the POA may not be cancelled or revoked upon the death or resignation of this director, because there is always a director available in the company.

The director is acting on behalf of the company and not on his own behalf.

The POA will become Null and void on death of the principal.

And also in case the director resigns from the company. 

Remaining Directors can call for a Board Meeting of the Directors and through unanimous resolution to give effect to the exit of Third Director from the Company, they can nullify the decisions taken and the documents executed by the Third Director who is either dead or left the Company. Remaining Directors have the vested rights to take any decision or to alter the decisions taken or documents executed by the Third Director.

Please note that the said Power of Attorney will not get cancelled automatically. Once the resolution is passed, remaining Directors can complete the compliance with ROC for removal of his name from the Board.