It is very difficult to find accurate statistics on divorce, and differences between countries are so great that any answer can only be useful from a specific countries' perspective. Finding prevalence statistics specifically focused on shidduchim is even harder. On of the problem of using divorce statistics is that part of the high reported rates of divorce is that people who get divorced also can remarry, and remarriages tend to be less stable than first marriages. This inflates the overall divorce statistics.
A published study by Kennedy and Ruggles in 2014 seems to suggest that the high rates of divorce have dropped after the 90's (as defined as the percentage of ever-married persons who have ever been divorced or separated, as opposed to the incidence of divorced. Their study shows that in 2010 the divorce rate amongst people aged 20-24 is around 15%, and steadily climbs to about 45% peaking at ages 50-54.
“Like the statistics on the incidence of divorce shown in Fig. 4, the
prevalence statistics in Fig. 5 show a decline in marital instability
from 1980 to 2010 among younger ever-married people. This decline is
more than cancelled out, however, by a massive increase among persons
in their 50s. By 2010, almost one-half of ever-married persons had
been divorced or separated by the time they reached their late 50s.
The shifting age pattern of divorce suggests a cohort effect. The same
people who had unprecedented divorce incidence in 1980 and 1990 when
they were in their 20s and 30s are now in their 40s, 50s, and 60s. The
Baby Boom generation was responsible for the extraordinary rise in
marital instability after 1970. They are now middle-aged, but their
pattern of high marital instability continues. As Brown and Lin (2012)
pointed out, part of this may simply be a consequence of the high
divorce rates that they experienced earlier in life, given that
remarriages tend to be less stable than first marriages.”
source: Kennedy S, Ruggles S. (2014). Breaking Up Is Hard to Count:
The Rise of Divorce in the United States, 1980–2010. Demography,
51(2), 587-598. doi:10.1007/s13524-013-0270-9.
These rates contrast somewhat with the closest study that specifically focuses on the demographics of religious groups and that is the 2014 pew religious landscape study.
It reports that 9% of the american jewish population is divorced or separated, but this number is difficult to compare to other studies, because it merely surveys who is married and who is divorced, and is not comparable to a divorce rate.
More problematic is that it doesn't answer your question about the success of shidduchim, because this statistic (or the pew study in general) distinguishes between jews who used matchmakers and jews who found partners 'naturally'. I am not aware of many studies that focus on divorce rates in marriages due to shidduchim. The one that I know of shows the rate of divorce in Israel (not comparable with the numbers shown above) and then: only in the haredi community, which is such a specific community that it is very difficult to extrapolate it to the larger jewish community that makes use of shidduchim. It would seem that in this specific haredi population in Israel the divorce rate is relatively low: lower than found in most other western countries. Caution must be excercised in comparing the rates, because the haredi community is different in many respects to the general (jewish) populations that are part of census data in other countries.
The study by Greenberg, Buchbinder and Witzum in 2012 cites a study from 1995 and states:
“Consistent with these values, the population census carried out in
Israel in 1995 found that being single was relatively rare in the
ultra-orthodox community: among those aged 25–34, 12% of
ultra-orthodox males were single in contrast with 35% of
non-ultra-orthodox males, while only 5% of ultra-orthodox females were
single in contrast with 20% of non-ultra-orthodox females. Although it
is not difficult to divorce in ultra-orthodox society, the sanctity of
marriage (and the difficult aftermath of divorce for a couple with
many children) may contribute to the relative rarity of divorce: in
the 1995 census, 1.3% of ultra-orthodox males were divorced in
contrast with 3% of non-ultra-orthodox males, while 1.5% of
ultra-orthodox females were divorced in contrast with 6% of
ultra-orthodox females. Further, the average age at first marriage for
ultra-orthodox males was 21.3 years (27.2 for non-ultra-orthodox
males), and for ultra-orthodox females it was 19.9 years (24.8 years
for non-ultra-orthodox females) (Gurovich & Cohen-Kastro, 2004). “
source: Greenberg, D., Buchbinder, J. T., & Witztum, E. (2012). Arranged matches and mental illness: therapists’ dilemmas. Psychiatry, 75(4), 342-354.
So, to try to answer the question; No, it does not seem to be that there are recent statistics. The closest peer-reviewed shidduch-specific statistics seem to be around 20 years old, and people with access to israeli census data might find more recent data. Regardless, it seem that in haredi communities divorce rates after arranged matches are low, but it is nigh impossible to extrapolate this to the broader community of jews that use shidduchim, and difficult to compare them to non-shidduch marriages and countries.
In the end, even if there would be data that would allow for in-country in-cohort comparisons of the succesrate of marriages between shidduchim and 'regular' marriage, the problem would still be that no such comparison on natural groups can be made in good conscience. To say that one factor is the actual cause of an observed phenomenon ideally one would have two groups that are exactly alike and in which only the supposed cause varies. In natural groups this is not the case. The community that uses shidduchim is notably different from other groups in the values they hold, family dynamics, etc. No amount of statistical correction can truly remove these systematic differences between groups. Any comparison should be made with great caution
