Can I say: "O Allah send our greetings to our Prophet and bless him" whenever I forget something.

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions. Allah Commands us to invoke blessing upon the Prophet Muhammad (Peace and blessing be upon him). Allah Says (interpretation of meaning): {Allâh sends His Salât (Graces, Honours, Blessings, Mercy, etc.) on the Prophet (Muhammad SAW) and also His angels too (ask Allâh to bless and forgive him). O you who believe! Send your Salât on (ask Allâh to bless) him (Muhammad SAW), and (you should) greet (salute) him with the Islâmic way of greeting (salutation i.e. As­Salâmu 'Alaikum).}[33:56]. The Prophet also ordered us to invoke blessings upon him. Therefore, invoking blessings upon the Prophet is a kind of worship, which is not restricted to a certain time. So, at anytime it may be proclaimed. But, to limit it to an occasion and whenever that occasion occurs one invokes blessings on the Prophet is an innovation. In fact designating a certain time or place to worship Allah other than what is proved from Shariah is Bidah (innovation). Though being accustomed to invoke blessings upon the Prophet at the time of selling, purchasing or forgetting might not be a form of worship rather it is merely a custom and an expression of astonishment. Some scholars consider, invoking blessings upon the Prophet at the time of selling, as Bidah. (See Tasheeh ul-Du'a Sheik Bakar Bin Abu Zaid). We could not find the opinion of scholars regarding invoking blessings upon the Prophet at the time of forgetting, but it is apparent that the rule of Bidah (innovation) applies to it. Allah knows best.