Short Answer:

We have enough evidence to say that there was a reasonable likelihood that a Roman soldier would survive to retirement, but whether that's a %50 chance, less or more-- would vary from place to place and from time to time. The evidence we have suggests that the Romans themselves thought they had a good chance of surviving to retire.

Discussion:

it seems to me that a life of battle after battle . . . would leave a fairly small percentage of legionnaires surviving

Don't assume that. Romans fought many battles, but soldiers spend a lot of time just waiting around, then and now, and we've got plenty of evidence for Roman soldiers surviving to retire, and plenty of evidence that their life wasn't one of constant warfare. It's quite possible that a Roman soldier might have served many years without participating in any major military encounter.

We've got lots of surviving examples of soldier's leisure time pursuits, including the wonderful Vettweiss-Froitzheim Dice Tower which bears the inscription: "PICTOS VICTOS HOSTIS DELETA LVDITE SECVRI" ( = "The Picts are defeated, the enemy destroyed, play in safety"). We've also got another dice tower from a Roman fort at Richborough in England; it seems that being a legionary included quite a bit of dicing and gambling. Its striking how often you see references to dice games in a Roman military context, including most famously, Julius Caesar's (per Suetonius) "alea iacta est"

Roman military camps with their celebrated attention to sanitation were likely much cleaner places to live than cities -- we've got evidence from graves that people lived longer outside cities than in. Romans took cleanliness seriously, soldiers no less than civilians

The long history of excavation of permanent military garrisons has demonstrated that bathing facilities were considered an essential part of military life in Roman Britain. With examples from the South Coast to the Antonine Wall, it is easy to approach baths as an expected part of a fort or fortress

In the Res Gestae Divi Augusti -- a bit of regime burnishing puffery "the Deeds of the Divine Augustus" -- it is claimed that Augustus paid out money and/or land to some 300,000 out of the 500,000 in his service as praemia militiae ( = "military rewards"). I wouldn't be too confident in that number -- the Res Gestae is very clearly an official bit of public relations-- it's not easy to come up with a better one, but we have some clues, albeit circumstantial.

We've got reason to believe that Roman legionaries as a category would be healthier than average-- they're men who by definition hadn't died in childhood, and were capable of marching 20 miles with a heavy pack, which is still a reasonably good way to identify someone in good physical condition. As adults, they'd be beyond many of the deadly childhood illnesses, they'd continue to drill, be well fed. A healthy fit 20 year old typically doesn't require any modern medical intervention to make it to 45; on the other hand an infected wound or diarrheal disease would kill a man who would be readily treated today.

One bit of evidence is that facing a shortage of recruits, we can find on occasion the Romans extending military service -- as for example in the year 5 CE, when we have it on Cassius Dio's account that service was extended in exchange for a payment. This suggests that there were substantial numbers of soldiers still fit for duty and at their erstwhile retirement age.

A second bit of evidence are various memorials. The Romans had a helpful habit of telling us quite a lot about themselves in funerary inscriptions, and when we look at those for soldiers, we find quite a number of veterans.

Yet another bit of evidence are Roman military diplomas, of which something on the order of 800 made of bronze survive. That's not a lot, but it's not rare either. We also know of the existence of the Collegia Veteranorum, a mutual aid organization for veterans; they had an important role in assuring the veteran's proper burial at his death. The existence of these organizations is good evidence for substantial numbers of soldiers surviving to retirement. We also have evidence of a kind of forced savings plan, apparently administered by the signiferi that would serve as a kind of pension for those who had to leave the service before attaining veteran status; that this is a kind of "safety net" implies that it was the less common expectation.

Putting together all these pieces of evidence has allowed scholars like Eric Birley to build outlines of Roman military careers. I believe the present record for "longest serving Roman soldier that we know of" is presently held by one Aelius Silvanus who apparently served some 60 years!

I have been waiting for some enterprising historical demographer to assemble these data and do some statistical modeling-- as yet haven't seen a paper, but I'd expect that with the data we have someone may eventually be able to give you a more precise answer than "a lot of veterans survived to retire" -- but at present that's about the best we can do.

Sources:

COBBETT, R. E. “A Dice Tower from Richborough.” Britannia, vol. 39, 2008, pp. 219–236.

Revell, Louise. “Military Bath-Houses in Britain: A Comment.” Britannia, vol. 38, 2007, pp. 230–237.

Brunt, P. A. “Pay and Superannuation in the Roman Army.” Papers of the British School at Rome, vol. 18, 1950, pp. 50–71.

Bennett, Julian. “New Evidence from Ankara for the Collegia Veteranorum and the Albata Decursio: In Memoriam J. C. Mann.” Anatolian Studies, vol. 56, 2006, pp. 95–101.

Ezov, Amiram. “The Centurions in the Rhine Legions in the Second and Early Third Century.” Historia: Zeitschrift Für Alte Geschichte, vol. 56, no. 1, 2007, pp. 46–81.

E. Birley, "Promotion and Transfer in the Roman Army, ii: The Centurionate", Carnuntum Jahrbuch, 1963/4, 21-3

Goldman, Andrew L. “A Pannonian Auxiliary's Epitaph from Roman Gordion.” Anatolian Studies, vol. 60, 2010, pp. 129–146.

Mellor, Ronald. “A New Roman Military Diploma.” The J. Paul Getty Museum Journal, 6/7, 1978, pp. 173–184.

Ginsburg, Michael. “Roman Military Clubs and Their Social Functions.” Transactions and Proceedings of the American Philological Association, vol. 71, 1940, pp. 149–156.