Here's some tips on how to re-access your Cydia account so you can download your past purchases from another device.
This is for jailbroken iPhones. If you don't have a jailbroken iPhone, ignore this post.
First off, make sure to have your Google or Facebook account login info which is associated with your Cydia. If you don't have that, you're out of luck.
Next, go to this URL on your phone: https://repo.packix.com/account/
Next, press the appropriate button on the screen to sign in.
Once you're signed in, click on "Add Device" to the right of "Linked Devices".
Once there, click on the "Cydia" button.
Then you will see "Open Cydia to Share URL". Click that. When "Open in Cydia" pops up, confirm that.
This will take you over to Cydia and you'll see that you're on the Sources menu.
Then click on "Continue to Source" om the main screen, but note that Cydia has a bug where it will grey it out if you just click it normally. Instead, click and kind of swipe right at the same time, and it will work. If this fails, just press "Reload" at the top and try again.
Now click "Sources" at the bottom of the Cydia screen and verify you see "Packix" there.
At this point, close Cydia and restart it.
Then you'll click on "Manage Account" on the home screen, noting that same swipe-right-while-clicking method to do it.
Then click on the type of account you want to log in with (Google or Facebook), and at that point, everything should be linked, and you'll be on your way.