'become forgetful' is correct and usable in written English.
You could use it in a sentence such as "Sometimes, as we get older, we can become forgetful of recent events."
I've become forgetful, too.
They might go crazy, become forgetful.
I'm worried I might become forgetful, and there's a lot of words in our songs".
I had to tease things out of her, and I always hoped, with time, she'd soften, become forgetful and tell me more.
Still other researchers are studying identical and fraternal twins to discover whether some people are genetically programmed to become forgetful with old age.
Animals get a collar.The angel is intended to look after old people who have become forgetful and young children who have become too adventurous, as well as dogs who are too interested in the bitch next door.
He became forgetful in his early 50s.
She became forgetful, running up credit card debts and not paying the bill.
She answered questions confidently and knowledgeably when it was of benefit to her, but suddenly became forgetful and confused when it was not, the judge wrote.
She will seem a familiar character to many readers here not because she was a historic figure, but because she has become unsteady, forgetful and diminished.
Yes! Statins seem to be weird medicine….People I saw before taking statins had only one problem – medium to high cholesterol levels but after taking them for awhile they seem to become very forgetful.
