It appears your affected order was paid via PayPal, so the buyer's shipping address was collected on PayPal's checkout site, rather than any checkout page we'd manage. When PayPal completes the buyer's payment, they transmit IPN (Instant Payment Notification) back to our system disclosing the order details (including any shipping address), so we can process the order for you.
It appears IPN does not provide a separate field for the second address line, so PayPal just combines both lines into the single 'address_street' field they do transmit. They document that field as supporting up to 200 characters max., so anything longer than that would get truncated, and thus buyers are advised to put their actual street address on the first line and any supplemental info (such as a company name or suite/apt. number) on the second line.
That said, the truncated address you provided us via email is considerably shorter than that 200 char. max., so length would not seem to be the reason that got truncated. To help us investigate this and determine whether we or PayPal truncated the address, we'd like to see the actual IPN PayPal sent us. We've already emailed you with further instructions, so we'll just continue our discussion there.