Well, being in danger of running out is more or less the point of the week-long refresh structure. It's an idea to prevent the 15 minute wizard day and the like. Also, it's quite possible (probable, for an Overlord), that one of the companions is a mage, which further alleviates the "can't do anything" worries. If a Necromantic class finds itself completely tapped out for resources, it's focusing a little too much on short term casting.
Wouldn't the weekly structure make it a 15 minute work week instead of a work day? As I understand it, part of the issue behind the 15 minute work day problem is that with the limited daily resources, you only have the spells/PP/whatever to work at peak capacity for a relatively short amount of time compared to your refresh time, doubly so if you decide to use your resources at a faster rate in order to eke out more power ("going nova").
The emphasis on longer-duration effects is a partial solution to this. It deals with the issue of temporal concentration of power (your buffs last all day/week/eternity, so they are always spread across later encounters). It does not address the issue of having nothing to do once everything's been cast; a spellcaster pulls out the crossbow just the same whether the spells he cast were instantaneous fireballs or day-long buffs that are still in effect. You need some sort of always-available abilities (per-enounter, at-will, or just some sort of slow and limited replenishment of the primary resource for use with more immediately useful magic) in order to avoid that awkwardness. Having a minion who still has gas isn't enough if the minion acts independently, because that still leaves those same unused spell-less spellcaster actions. The character + the character's features (ie: minions) might be contributing each round, but the character alone would not be, which is, as I said above, awkward
1. From what I remember of what you've discussed elsewhere about the various necromantic classes, and about Arhosa spellcasters in general, you were planning on giving them some more active basic abilities to use when not throwing necros around, which should deal with this just fine.
1. I can attest to this from personal experience. I played a Cleric/Marshal focused entirely on supporting the rest of the party, relying on a Warblade cohort for my more active contributions. When the cohort was working out just fine and the auras and buff spells were running, it was not fun to have the main character having nothing useful to do from round to round, even though I was still contributing both passively and, indirectly through the cohort, actively.
Another issue that I don't know if you've discussed is the sheer length of time that 1 week is for an adventurer. In a full-fledged dungeon crawl, with the standard average of 4 encounters/day and 13.3 encounters/level, 1 week can be the span of 2 full character levels. In practice, it tends to work out as somewhat less, closer to 1.5 character levels from my experience, and non-dungeon crawl adventures (such as the Red Hand of Doom module) frequently have more downtime, meaning that a week can be from 0.5 to 1 character level (plus or minus in more extreme cases). The choices you make in spending your grave tokens can easily be in effect a full character level later. If you overspend your grave tokens early (a particularly difficult fight, perhaps, or just poor budgeting), you might be unable to correct your mistake until you've leveled up once or twice. When you're going up against intelligent enemies that can adapt, walking away for a week to recover tends not to work out so well (much like taking an unplanned, non-vacation week off of work in real life).
Might there be some way to generate temporary grave tokens? It may alleviate some of the problem of running out of your weekly grave tokens if you invest more in the instantaneous necros rather than the week-long buffs, and since they'd expire quickly they'd avoid long term problems. The problem is the capacity for loading up more on long-duration buffs, so spending temporary tokens might result in a sharp reduction in Necros duration to compensate.
This might just be too needlessly complicated to be useful, but I can't help but be concerned even given the fact that most Necromantic characters will have a single minion they can order to fight for them even if they're run out of tokens for the week. Mostly it's just a late-night, rambling thought. Feel free to ignore it.
If some sort of temporary grave token system does get implemented, preventing long-term buffs could be done by having ongoing necros paid for with temporary grave tokens end when the temporary tokens would go away, essentially capping a necro's duration at the duration of any temporary tokens used to pay for it. So you could put up a week-long buff using 5 minute tokens, but the buff would only last for 5 minutes instead of the full week.