Ultimately, I'm trying to figure out if NASA's decrease in funds is responsible for fewer missions...
The decrease in launches and/or planned missions is due to budget cuts.
...what the funding required to keep those missions alive ...
The operational cost of maintaining contact with and retrieving data from any given spacecraft depends upon the age of the spacecraft and distance of the spacecraft from Earth. The former cost difference results from differences in designs/software/specs/etc. than the newer spacecraft (things change with time), which requires different personnel. Sometimes this can decrease the cost if things are simple and well understood by a younger, less senior engineer. Other times it can increase the cost if the only people that still understand such things happen to be very senior level engineers. It really depends upon the team and the mission.
The latter arises from the costs associated with maintaining and using either the Deep Space Network or the Near Earth Network. Using the DSN is expensive for several reasons that involve the use and maintaince of large area antennas, power, security, etc.
In general, operations costs are typically more expensive for spacecraft located farther from Earth than nearer (not always true, but a decent hand-wavy guideline).
...or if it's that the current missions cost more...
Yes, newer missions can cost more than older missions, but this is not always true either.
Changes in Requirements
Much of the reason for the increased cost is due to the decreased risk requirements. Meaning, newer missions are often held to a very high standard where failure is effectively not an option. The result is an increase in redundancy, testing, and quality of parts. Another significant fraction of the increased cost came from the increased price of launch vehicles bought from the United Launch Alliance (ULA).
Early Space Age Advantages
In the early days of the space age, missions were often approved based upon ~3-5 page proposals and they were designed, tested, and constructed by small teams (often a dozen or less university faculty and researchers). The missions had a lot of risk (i.e., little-to-no redundancies and/or the instruments being flown had no previous flight experience in space), were typically smaller thus requiring a smaller (i.e., cheaper) launch vehicle, and many missions flew fewer instruments. Most of the earlier missions were just much more simple in design and scope.
Changes in Opportunities
There has also been a significant decrease in the number of small explorer program (SMEX) and explorer program mission opportunities. Many of the recent (i.e., last ~10 years) announcements have been for the much larger and more complicated Flagship Program missions. These are more expensive for multiple reasons and the larger price results in fewer SMEX opportunities because there just isn't enough funding.
There are a semi-infinite number of reasons for why newer missions can be more expensive, but budget cuts often affect different parts of NASA differently. Sometimes budget cuts are specifically directed at one program (e.g., when congress cut funding for the manned spaceflight programs) while other times it is an across the board cut.
Regardless, you can see for yourself that NASA's budget peaked in 1966 and has been steadily declining since the mid 1990's until the most recent fiscal year, where the budget slightly increased.