The seismometers were part of the Apollo Lunar Surface Experiments Packages (ALSEPs), which were powered by radioisotope thermal generators. RTGs use the heat from decaying radioactive elements to produce power, and gradually produce less energy over time as the isotopes decay into more stable elements. By 1977 the ALSEP RTGs were only producing enough power to run either one experimental package or the radio transmitter at once; they probably would have stopped working altogether in a few more years anyway and it's better to have a controlled shutdown rather than a failing radio transmitter cluttering up the airwaves. Wikipedia also mentions "budgetary considerations", and apparently they wanted the ALSEP control room for another project as well.
Edit: I've just found [1], which adds a few additional details: first, they were designed for a lifetime of one year, so 1977 was well beyond their expected activity; and second, after they were decommissioned they continued to send carrier signals (but no data) which were used for various purposes.
They were using Plutonium 238, which is the most common RTG fuel. The Wikipedia page on RTGs has a fairly comprehensive overview of the possible candidate fuels[1]; one advantage of 238Pu is that it requires the least amount of shielding, an important consideration when launching things into space.
Pages 101-105 of the termination report I linked to above have the power output curves for the various RTGs, showing the decay curve (1 lunation ~= 1 month).
Edit: I've just found [1], which adds a few additional details: first, they were designed for a lifetime of one year, so 1977 was well beyond their expected activity; and second, after they were decommissioned they continued to send carrier signals (but no data) which were used for various purposes.
[1]: https://www.hq.nasa.gov/alsj/HamishALSEP.html
More detail than you ever wanted to know can be found in the ALSEP termination report: https://nssdc.gsfc.nasa.gov/misc/documents/b32116.pdf