I enjoy playing Standard and would like to compete on a more competitive level but I am apprehensive of paying, as an extreme example, $25/card for 4 Mutavaults or Sphinx's Revelations, only to have them either not be reprinted in the next block or banned altogether. I was told that WotC has become a lot more judicious in the last several years so that they rarely need to ban a card anymore due to brokenness/overpower. This does not completely alleviate my concern so I would like to know if there is any kind of resource that is known to fairly accurately predict which cards will stay around in the next block and which cards won't?
You have very little to worry about for standard in terms of banning cards. Standard is a very carefully designed format with a card pool small enough for wizards to have a very good grasp of the format in their internal testing phases. Every time they have banned a card they have learned from it, and the bans in standard are very few and far between.
The 2 specific cards you mentioned will not be banned in standard. This is because there is not another opportunity to ban them before they leave the format, which brings me to the more important part of my answer
Players worried about the cost of cards in standard should worry far more about Rotation than banning, because rotation is a much more likely thing for standard staples (heavily played, format defining cards) than banning. Both Mutavault and Sphinx's Revelation are in sets which leave the format in the Autumn/Fall of this year (2014) and as such, particularly given how big an impact they have had on the format, are very likely to rotate, and not be reprinted back into standard.
Wizards tend to avoid having high power cards which people play with/against a lot over a rotation period reprinted. There have been times where they have regretted reprinting staples, such as the Titans cycle of magic 2011/magic 2012 (the poster boy of which was Primeval Titan).
The vast majority of the time, when it comes to rotation, you should assume that every card of value is rotating. This is because that is almost always the case. Each set or block has a specific theme with a different mix of mechanics, and while some cards (mostly in the core sets) are reprinted, most of the time there is no guarantee that a card from Return to Ravnica block or Magic 2014 will be around this time next year. The cards that DO get reprinted, tend to be very low value, as they have usually been reprinted many times before. Take Doom Blade as an example for this. Even cards like that take a few seasons off, as Doom Blade did in Magic 2013.
Standard is a format that Wizards try to fundamentally change once a year, and they do that by removing a lot of cards and replacing them with totally new ones which do very different things (or the same things in different ways). If you are interested in playing standard at any sort of competitive level, then you will need to make yourself quite aware of what cards are rotating when, and either:
One thing to note which does have some impact on the above, is that while most staples will rotate out of standard, they will not become worthless. Older formats like Modern or Legacy often have a significant impact on the cost of cards. Mutavault is an example of a reprint of a staple in older formats, which is part of why it's price was so high so early, it has a proven track record. Similarly, some cards will not lose much (if any) value on rotation. Deathrite Shaman is a perfect example for this, Deathrite has a significant presence in Modern (or did, until he was banned) and Legacy decks - where his abilities are much more easily leveraged - but sees very little play in standard. The majority of his price is based on these formats, and as such will change little on rotation. Similarly, many of the strongest cards in Standard will go on to see play in Modern and Legacy, and as such lose much less value on rotation, or rebound from the dip very quickly.
Overall, bans are much less frequent, particularly in standard, than rotations. Additionally, the wide reaching nature of rotations makes them much more important to consider than bans when looking at the investment you are willing to make.
As Patters says, you should not worry about cards in Standard getting banned. From 1996 to 2014 (18 years), there have been a grand total of 27 cards banned from Standard/Type 2:
As far as reprints go, there is no perfectly accurate way to predict what will be reprinted and what won't. In general:
Mutavault and Sphinx's Revelation are unlikely to be reprinted in M15 or "Huey"/"Dewey"/"Louie" (the code names for the next three expansion sets). Unless we return to Lorwyn or have a tribal-heavy block (which we just recently had with Innistrad), I would even say a Mutavault reprint is unlikely in "Blood"/"Sweat"/"Tears" or "Lock"/"Stock"/"Barrel". Sphinx's Revelation is a fairly unique combination of effects (there are only 7 cards that I find removtely similar, and several of those aren't W/U) as well as being tied in with sphinxes, which aren't super common across the multiverse (while one of the Ravnican guilds is lead by a powerful sphinx). I would not expect a reprint of Sphinx's Revelation in Standard until and unless we have a Ravnica 3: The Movie the Book the Show. (It's possible we may see it in a set or precon not in Standard, such as the Commander decks or in Conspiracy.)
If we do ever return to Ravnica again, it will not be until after "Barrel"; Mark Rosewater said that revisiting the plane for a third time was not in the five-year plan.