I think your problem is in the starter solenoid. I've encountered this many times. If the starter clicks but does not engage, but will if you try enough times, it is not the battery or the connections. You need to remove the starter and dismantle the solenoid. Look closely at how the solenoid works. If it works that way I think it does you will notice that there is a terminal on each side of the solenoid that the main power to the starter runs through. When you turn the key to 'start' the solenoid is energized and a 'ring' slides up and makes contact with an L shaped copper washer on each side of the solenoid. This allows the power through to the starter motor and away you go. What often happens is that the two copper washers wear at different rates for some reason and then start to fail to make a good enough contact to allow the voltage through. The ' click' you hear is the solenoid 'ring' sliding up and hitting the contacts, but unfortunately it is only hitting one of them. The reason it will, or may, eventually work is that each time you try it the ring comes up in a slightly different angle and may make a good enough connection. What usually happens is that you have to try a few times, and then more and more and eventually it will just click away and never make contact. You should be able to purchase the copper L shaped washers for less than $10.00 and it is relatively easy to replace them. I've saved lots of people from the expense of a new starter with this simple repair.
Do not confuse this with the repetitive clicking that will occur if you have a bad battery or connections. That is a different problem. I believe your problem will be solved by repalcing the L shaped contacts in the solenoid. I hope so anyway. Good luck with it!!
1990 Prostar 190, 351 Indmar SO, bought as an empty shell and rebuilt over the winter (04/05). Sold in May 2009
New boat - 1993 Prostar 205. Bought in better shape than the 190 was but still needed some work.