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A few evidences may show people are inclined to use godan verbs more often.
ら抜き言葉 refers to making a "wrong" potential form from ichidan verbs as if they were godan verbs.
Recent verbs coined from loanwords or onomatopoeia are usually godan verbs.
In addition, some people on the net like to jokingly use the wrong imperative form for ichidan verbs as if they were godan verbs. On sites like 2ch you may find people saying よく見れ or やめれ instead of よく見ろ or やめろ. (Note that these are still jokes like "All your base are belong to us.")
These may indicate ichidan verbs may become unpopular far in the future. Still, I'm not aware of any ichidan verb that was turned into godan completely. Except for the ら抜き, the conjugation rule for ichidan verbs are well preserved, and no one say 見らない or 食べります, for example.
EDIT: According to this entry, 蹴る was an ichidan verb in archaic Japanese, but somehow merged into the godan verb family in modern Japanese. Many people are still confused with the imperative form of 蹴る. Nevertheless, such a conversion seems to be very rare in the history.