I think that the answer lies in how the Church understood the nature of the Eucharist. Whereas Passover was essentially a commemoration of an event of the Exodus, the Eucharist is something entirely different. According to the account in Exodus (12:14), Passover was instituted strictly as a memorial. Christ Himself described the nature - and necessity - of the Eucharist:
John 6:53 (KJV 1900)
Then Jesus said unto them, Verily, verily, I say unto you, Except ye eat the flesh of the Son of man, and drink His blood, ye have no
life
in you.
I am not aware of any early Christians who maintained that the Eucharist should only be celebrated once a year in lieu of the Passover meal (though I am sure there probably were some). There are writings, however, of certain Church Fathers explaining the need for frequent (i.e. more than once per year) Communion. John Cassian (5th c.), a western Church Father with an eastern upbringing wrote:
We must not avoid communion because we deem ourselves to be sinful. On
the contrary, we must approach it more often for the healing of the
soul and the purification of the spirit, to show our humility and
faith, by considering ourselves unworthy and in need … that we desire
even more the medicine for our wounds. Otherwise it is impossible to
receive communion once a year, as certain people do … considering the
sanctification of heavenly Mysteries as available only to saints. It
is better to think that by giving us grace, the sacrament makes us
pure and holy. Such people who receive less often manifest more pride
than humility … for when they receive, they think of themselves as
worthy. It is much better if, in humility of heart, knowing that we
are never worthy of the Holy Mysteries we would receive them every
Sunday for the healing of our diseases, rather than, blinded by pride,
think that after one year, receiving once or twice yearly, we become
worthy of receiving them.
Conferences of John Cassian, Chapter XXI
Similarly, John Chrysostom (4th c.) commenting on those who did not receive the Eucharist at the weekly Liturgy, wrote:
Look, I entreat you: a royal table is set before you, angels minister
at that table, the King Himself is there, and yet, you take no account
of it. Are your garments clean? Then fall down and partake! For
everyone who does not partakes of the mysteries is standing here in
shameless falsity. When you behold the curtain drawn, then imagine the
heavens are let down from above, and that the angels are descending!
Why stay at liturgy and yet not partake of the table? I am unworthy,
you say. Then you are also unworthy of that communion you also have in
prayer. Come!” Holy Father
Commentary on the Epistle to the Ephesians, Homily III
These writings, although not by the Apostles themselves, might help to explain why the Eucharist was seen by the early Church as something more than an annual replacement of Passover.