I notice a lot of stocks aren't offering options for May. Many aren't offering for May and June. Is there any reason for this gap?
This is explained at Investopedia:
When stock options first began trading, each stock was assigned to one of three cycles: January, February or March. There is no meaning as to which cycle a stock was assigned - it was purely random.
Stocks assigned to the January cycle had options available only in the first month of each quarter: January, April, July and October. Stocks assigned to the February cycle had only the middle months of each quarter available: February, May, August and November. Stocks on the March cycle had the end months of each quarter available: March, June, September and December.
As options gained in popularity, it soon became apparent that both the floor traders and individual investors preferred to trade or hedge for shorter terms. So the original rules were modified, and in 1990, the CBOE decided that every stock would always have the current month plus the following month available to trade. [...]
Every stock has at least four expiration months trading. Under the new rules, the first two months are always the two near months, but for the two farther-out months, the rules use the original cycles. [...] Under the newer rules, there is always the current month plus the following month available
So the reason why you see some stocks not offer options for May is because they are not on the Feb/May/Aug/Nov cycle. The stocks that aren't offering options for May or June must be on the Jan/Apr/Jul/Oct cycle. But all the stocks you are looking at offer options for March and April, because they have to offer options for the current month (March) and the following month (April).
Although there is a historical answer to your question, you can call the CBOE and request series be added. It is essentially a click of a button for them at this point, and there is little to no red tape involved. Just don't say you are a retail investor on the phone/email (so you might need to make something up), because nobody on wall street is interested in someone that is simply saving 10% of their income for five decades. CBOE wants to believe that there will be a market for the options they list.