I realize one can use Excel, but I was looking for something specifically developed for this purpose.
I've since found one, but would like to look at others if there are any. LifeCheck is the one I've found; looks quite good.
I took a quick look at the LifeCheck website, but it only appears to consider mileage in tracking component life. While this simplistic approach may be satisfactory for some uses, for other components that are very highly stressed and/or whose failure in service may create a hazardous condition, a more sophisticated lifecycle tracking approach would be required. The remaining (fatigue) service life of a suspension or drivetrain component is determined by both the number and magnitude of accumulated load cycles, and these values can vary greatly for a given mileage, depending upon how the car was driven or what the track layout was for that accumulated mileage.
In the aircraft world, digital electronic Health Usage and Monitoring Systems (HUMS) are now widely used for monitoring flight/fracture critical components and systems. These HUMS systems use high-frequency instrumentation and data acquisition systems to record the operating loads and cycles for critical components, and then calculate the remaining service life of those components in real-time using sophisticated software.
While I don't think the application you have in mind would justify the expense of an aircraft-quality HUMS, you may still want to consider a system that has a greater level of sophistication than LifeCheck does. Given that there are lots of powerful, low-cost automotive/racing data acquisition and instrumentation systems available off-the-shelf, it would seem to pose no problem collecting whatever amount of data you need. The only other information you would require is a load/lifecycle characterization of each component to be monitored. The data downloaded after each session/race would be added to the totals for each component in the database and the remaining service life would be recalculated. Calculating fatigue life in metal structures requires a bit of specialized knowledge in stress, metallurgy and statistics, but it's not beyond the technical grasp of most mechanical engineers.
And if there are no commercially available applications that meet your particular requirements for technical sophistication and cost, you may be able to make some money filling a market niche.