Finding initial parameters for fitting nonlinear functions is crucial except in very simple cases with few parameters. The more parameters, the higher the chance the fit will not converge due to even slight mismatches of the start conditions. So what you see is a general problem of nonlinear fitting.
One possibility to increase chances is first to analyze the function: where is the maximum, is it possible to determine a half width of lifetime (exponential growth/decrease), and then calculate numerically some characteristics of the data set before starting the fitting procedure: 1st, 2nd derivative etc, and from these information estimate one or two parameters. Sometimes, functions such as PeakDetector may be useful here.
In a second step, still before starting the fitting procedure, one could calculate the difference between the model function (with the initial starting parameters) and the data set, and then inspect this difference: is the maximum of this difference to the left or to the right of your model function? Then adjust the peak position, etc.
This is a general and complicated problem, so do not beome desperate: the differences between many commercial programs are exactly how sensitive or tolerant they are, that is, how smart they are to find initial guesses (the fitting precedure is standard)
One example: I used to fit Gaussians, with an offset, that makes 4 parameters. It hardly ever worked. Then I decided to determine the offset (usually there is always a region where no signal is to be expected) first, subtract it, and then use the Gaussian with three parameters only, without offset. This worked, most of the time. Then, if ambitious, one could just use these fit results to restart with four parameters...
Good luck,
Wolfgang
