Septic systems (drain fields included) last forever if the septic system is cared for properly. That's the key though.
If the drain field is "failing" wouldn't it take a few years to completely fail? The last pump lasted 2 years and 10 months. Wouldn't it make sense for the next one to be around 2 years, then 12 months and eventually 6 months?
I'm not a plumber, just have some experience with my own systems, so I might not be correct. Pumping the tank is only meant to remove the solid sludge at the bottom of the tank that accumulates with time/use. If not pumped, it gets to a high enough level and will start flowing out into the leach field, filling the drain lines, at the far ends first, then working its way back to the distribution box. The leach field will be losing its capacity to drain all the water that is flowing to it and you'll start getting problems with your tank backing up. I assume you'll experience it after heavy rains or as mentioned, the leaking toilet that put out an extra 10,000 gallons a month.
The tank only holds 1,000-1,500 gallons or so. Lets say the family uses 2,000 gallons per month--- it will only be 2-3 weeks before the tank fills and effluent starts flowing to the leach field. I suppose the ground would dry out in those weeks, allowing the lines to drain properly for a bit, so you'll have a working system for at least a month.
Since you mentioned a standing puddle of water at the tank, you've definitely got issues that I think pumping the tank won't fix. From what I understand, clogs in the leach field or distribution box don't clear up on their own and won't be helped by pumping the tank. If your lines aren't clogged, I wonder if the water table is high enough that the soil is just waterlogged (after lots of rain perhaps) and won't allow proper drainage.
The ground is all sand. I can dig with a shovel. If I was to do it myself, it would probably take me 2 days to do the digging and another 1 day to replace the pipes. If they quote me more than $2500, I think I would prefer to do it myself.
My first septic experience was with my dad, one of his work buddies, and my brother when I was about 12 years old. In NJ, a licensed contractor was required to do the leach field replacement and my parents were getting quotes around $10,000 (this would have been in the early 90's) Instead, my dad had a load of gravel delivered and had the pvc pipe and filter paper ready to go. We hand dug and replaced all the lines in a weekend. I have a feeling you're not going to get a quote as cheap as you'd like and if you do it yourself, you may need to see how to go about doing it incognito. And if its the problem is the soil itself, as in high water table, etc, not sure what to tell you. When the house was built, it should have passed a perc test.
edited to add--- Its worth mentioning that all the work we did eventually had to be redone. The water table was very high and the ground was usually soggy around the area of the leach field. Replacing the lines and adding gravel helped, but I remember when the house got sold about 5 years later, to pass the perc test, the contractor was required to dump enormous amounts of sand in the backyard, raising the entire drainage area about 2 feet or so, plus a pump because the leach field was now above the level of the tank.