Why does communion frequency vary in different denominations?

The Last Supper is practiced in many ways. Firstly, in some aspects, the Bible isn’t very specific. For example, the Bible says to dress modestly, but how do you interpret that? Some Churches dress in white cloaks, where as others just wear smart clothes. This leads to different denominations. Also, the Bible isn’t specific about if you should have alcohol in Church services. The Catholics tend to have wine where-as protestant Churches normally have grape juice. Again, this leads to more denominations! This is because different Churches are doing what they think is correct. Secondly, Catholic/ High Churches tend to celebrate the communion everyday where-as Low/Protestant Churches may celebrate it once a month. Lastly, there has to be different denominations because when Henry the 8th made the Church of England he had to differ the Catholic rules.

As DJClayworth said, there is some correlation to the position between "real presence" and "entirely symbolic", but that's not everything. "Entirely symbolic" understanding of Eucharist usually lead to lower communion frequency, but this doesn't have to be the case - the consequence of lower importance of the communion is especially that it's more arbitrary. This can lead to extremes remembered by Caleb, but usually it just means that "we are used to celebrate Lord's Supper once per month and we see no reason to change it". "Once a month" probably has some historical roots.

On the other hand, in Catholic Church in 21st and big portion of 20th century frequent communion is the norm. But it wasn't always like this! There were times when "once a week" was most usual (especially in the earliest times), when daily communion was normal like today, but also when it was hard to get to communion more often than once a month or once a year. There were theological reasons for all the practices - they were usually closely tied to views of God's love and mercy and of how much is man sinful. Jansenists, who focused on sinfulness and unworthiness of man, proposed rare communion ("People are not worthy of receiving such a gift ever. Well, we can allow then to go to communion once a year, if the do proper repentance."). On the other hand, Catholic theology today focuses more on God's love for us and His willingness to give Himself to us, and frequent communion is a logical consequence.

The reason for the different traditions of frequency of communion is that there are a wide variety of views within Christianity about what communion actually is. It is so widely disagreed over that Christians often can't agree over what name to call it. The different theologies give rise to different practices of communion, including different frequencies.

It would be far too long and complicated to discuss in detail the different views of communion here. This Wikipedia article gives a reasonable overview, and I will attempt to pull out some salient points.

The Catholic view of Mass (which differs slightly in a technical way from communion, but which we will treat as the same thing for this answer) is that in the Mass the body and blood of Jesus become actually present. Moreover the Mass is an actual sacrifice by the participants, by which the benefits of the sacrifice of Jesus on the Cross are made available to the participants. (I will state here, because of common misconceptions, that this does not imply that the sacrifice of the Mass either adds to or replaces the ultimate sacrifice of Jesus). While the details are complex, the implication of this is that participation in the Mass is beneficial in and of itself. This explains the Catholic practice of attending Mass frequently - once a week for normal members and even more frequently for priests and other religious. Each attendance brings with it benefits, and the more frequently it is done the better.

At the other end of our oversimplified spectrum is the view that communion is simply a memorial - a ritual in which each person remembers the sacrifice and death of Jesus. This was the view espoused by Zwingli, and is generally held by Baptists and similar churches. It is usually referred to as Memorialism. The benefit of participating in this memorial is limited to the extent to which it is helpful to the individual, producing thoughts and feelings that assist the participant's spiritual life. Because there is no intrinsic benefit to attending a service of communion, frequency of attendance is much less. It was thought that since the effects were dependent on the state of the participant's mind, then over-frequent attendance was counter-productive and seen as idolatory by the reformers.

Many churches hold different views to those, and they can roughly be arranged on a line from 'real presence' to 'entirely symbolic'. Frequency of attendance is typically reasonably correlated with being close to the 'real presence' end. Anglicans and Lutherans typically believe in the 'real presence' without necessarily endorsing the doctrine of transubstantiation, and typically celebrate weekly, with celebrations more frequent than daily being discouraged for everyone. Memorialist churches tend to celebrate once a month, or a few times a year.

I might mention a few outliers from this pattern: the Salvation Army, which does not celebrate communion at all (thanks to its origins in as a para-church rather than a church organization, and its strongly anti-alcohol stance) and the churches that associate communion strongly with the Jewish Passover, and celebrate communion once a year.

We know the very early Church shared communion at least once a week, from their specifically celebrating the resurrection on the first day of each week, and the description we have of them celebrating the sacrament whenever they were gathered together. By the middle of the fourth century AD the Eucharist was given in what is more or less the modern Catholic and Orthodox forms, though the various Eastern Rites probably developed slightly before the Latin Rite (ibid). The older weekly celebration corresponds more to the modern Sacramental frequency than to the Memorial frequency, which makes sense since the early Church held the Eucharist to be sacramental in nature (additional citation).