Is it possible to use both of these same type of adverbs together? Is this sentence correct?
Tom devient distrait. Il perd toujours ses clés ces jours-ci.
Toujours usually means that something holds continuously over time: it's true now, it was true a moment ago, it has been true for a while, and will continue being true for a while. This is similar to always in English.
Toujours indicates that something is true at every point in a time span, but does not provide any indication of what the time span is. Here, toujours is qualified by ces jours-ci (“these days”), which provides the time span.
(Toujours can also indicate that something was true earlier and has not stopped being true, like still in English. This is a separate meaning, not relevant here.)