Yes, it's still doable. You don't have to have panel data to use -reshape-.
Note: In your example data, there are only three values of reason, so only three curves result. Also, for two of those values of reason, there aren't enough data points to form a stairstep graph, so the result looks like a straight-line connect instead. Presumably in your full data you will not encounter these problems.
Code:
gen long obs_no = _n reshape wide survivor, i(obs_no) j(reason) graph twoway connected survivor* time, connect(stairstep) xlabel(15(5)35) msym(i)
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