"Eight digits" means 108 = a hundred million possible passwords. At best, you selected your password fully randomly, implying that the attacker, on average, will have to try half of them before hitting the right one (so fifty million connection attempts).
(The "at best" means here that the attacker always has the option of trying passwords in a random order, so there is no password selection strategy, however nifty it may look, that can make things harder than that for the attacker. Some selection strategies may make things easier, though. Therefore, in password generation, randomness rules.)
The important term above is "average". On any specific case, an attacker may get especially lucky or especially unlucky. However, the attacker can perform the same kind of computations and will decide to attack or not to attack based on his perceived, a priori chances of success. Also, not all attackers are completely rational in their decision-making.
How many authentications the attacker may attempt depends on the context and server behaviour. If the server uses "typical" hardware, implements inexpensive password processing (e.g. single SHA-1, not bcrypt), and does not limit authentication rates, then an attacker can hope for, say, 1000 authentication attempts per second, thus reaching the 50 millions in about 50000 seconds, i.e. about 14 hours. On the other hand, if the server locks out the account after 10 failed successive authentication attempts, then the attacker won't be able to try more than 9 attempts between any time you connect; if you connect on a daily basis, then the attacker's expected breaking time will be about 15210 years.
Since there is a lot of variation in how servers implement authentication, and in particular how hard they try to detect brute force attempts and how thoroughly they react to it, the only possible answer to your question can only be "it depends".