What is the situation called when we remember something suddenly which we forgot before

It could be involuntary memory or mind pops.

Or perhaps Eureka moment or epiphany.

The eureka effect (also known as the Aha! moment or eureka moment) refers to the common human experience of suddenly understanding a previously incomprehensible problem or concept.
[Wikipedia]

If not eureka or epiphany, try the following words/phrases:

• Retrieve would also work here. One of its meanings is to recall something (but sadly, it doesn't connote 'sudden remembrance'). However, you could say sudden retrieval or tongue retrieval.
• A moment of clarity which means a time when a person suddenly understands something.
• Breakthrough means an important discovery or event that helps to improve a situation or provide an answer to a problem, but I think it's too strong and doesn't work well in this context.
• Ferret something out means to find out a piece of information or find someone or something, after looking in many places or asking many questions but it also doesn't fit.
• Flash back to something means to suddenly remember something that happened in the past.
• Proustian: b) relating to or evoking the recall of a forgotten memory, but it doesn't connote 'sudden remembrance' either and is rarely used.
• The opposite of what you're describing is brain fart.... perhaps brain-spark or brain-jostle (opposite of brain fart)?

From Wikipedia on recall (memory):

A tip of the tongue (TOT) state refers to the perception of a large gap between the identification or knowledge of a specific subject and being able to recall descriptors or names involving said subject. This phenomenon is also referred to as 'presque vu', a French term meaning "almost seen". There are two prevalent perspectives of TOT states: the psycholinguistic perspective and the metacognitive perspective.

Psycholinguistics views TOT states as a failure of retrieval from lexical memory (see Cohort Model) being cued by semantic memory (facts). Since there is an observed increase in the frequency of TOT states with age, there are two mechanisms within psycholinguistics that could account for the TOT phenomenon. The first is the degradation of lexical networks with age, where degrading connections between the priming of knowledge and vocabulary increases difficulty of successfully retrieving a word from memory. The second suggests that the culmination of knowledge, experience, and vocabulary with age results in a similar situation where many connections between a diverse vocabulary and diverse knowledge also increases the difficulty of successful retrieval of a word from memory.[66]

The metacognitive perspective views TOT states simply as the awareness felt when such an event occurs and the perception of the experience involved. Mainly being aware of a TOT state can result in the rapid devotion of cognitive resources to resolving the state and successfully retrieving the word from memory. Such an explanation leaves much to be desired; however, the psycholinguistic perspective and the metacognitive perspective on TOT states are not mutually exclusive and both are used to observe TOT states in a laboratory setting.[66]

An incubation effect can be observed in TOT states, where the passage of time alone can influence the resolution of the state and result in successful recall. Also, the presence of a TOT state is a good predictor that the problem can be resolved correctly, although this has been shown to occur more frequently with older-young-adults than young-adults or seniors. This is evidence for both the metacognitive perspective as well as the psycholinguistic perspective. It demonstrates the devotion of resources to searching memory, a source of cumulative information, for the desired correct information, and it also shows that we are aware of what information we know or do not know.[67] This is why the current debate between the psycholinguistic view of TOTs as retrieval failure and the metacognitive view of TOTs as a tool for learning continues.

The topic of your question is not simple. Based on the above, I would call the situation you describe (great effort to recall something that you know only to remember it suddenly in the middle of doing other work) an incubation effect for a tip-of-the-tongue state. Not exactly an ELU matter.