I suppose a good number of illegal border crossers (illegal immigrants, criminals, asylum rejects, etc) would have to attempt to cross the border several times before either giving up or making it to the US side. So, for documenting purposes, for every attempt caught, how many repeated offence on average happened? Does anybody have the statistic? Kinda hard to find an obscure number through Google-ing.
The number of attempts before either getting past the Border Force or being caught has decreased markedly in the last 10-15 years. Most border-crossers either succeed on the first attempt, or give up after the first failure.
It was true that in the past, most people who were caught were returned to Mexico and just tried again, until they were successful. That is increasingly untrue. Research on this is difficult, as undocumented immigrants don't normally want to draw attention to themselves, but in a DHS report by Bryan Roberts (reported on in an azcentral article) he finds that the number of successful crossings has dropped to 10% of what it was in 2005, and the probability that an unsuccessful crosser will give up has risen dramatically, from about 10% to between 60% and 70%.
The probability that a border crosser will be caught has also increased, to about 50%-60%, and if caught the probability that the crosser will be prosecuted or detained has risen too.
From these statistics, we can estimate that of roughly 350,000 people who attempt the crossing, about half (175,000) will be successful on their first attempt. About 110,000 will fail and make no further attempts. About 30000 will succeed on the second attempt, and the average number of attempts will be between 1.25 and 1.5.
Heightened security at the border is a significant factor in this, as it makes it more difficult, and hence more costly to get past the border force, and hence reduces the number of repeat attempts. The report suggests that the price paid to smugglers has risen from $1500 to $6000. This high price deters repeat attempts.