"mantener en alta" is the opposite to "dar de baja"

deberá mantener en alta y continuar cotizando a la seguridad social del país de su sede = (I suggest)
shall/must maintain the social security scheme/system of the country of its headquarters and continue to make contributions to it

http://ec.europa.eu/social/BlobServlet?docId=1848&langId=en
The main exception is the option to maintain the social security scheme of the Member State in which the undertaking normally operates (the ‘posting State’) whenever the worker concerned is sent by that undertaking to another Member State (‘State ofemployment’) for a period of time which from the outset is limited (a maximum of 12 months, which may be extended by another 12 months) and provided that certain
conditions, to be discussed in the points below, continue to hold good.

…permit the person to maintain the social security scheme in that State must be based on objective elements other than those which characterise gainful employment.

http://eur-lex.europa.eu/Notice.do?mode=dbl&lang=en&ihmlang=...
While in Greece the right to continue to make contributions must be asserted within thirty days of receiving notification of posting by the worker, in the other above-mentioned countries there are no specific limitations to the exercise of this right.
Si bien en Grecia debe hacerse valer el derecho a continuar cotizando en el plazo de los treinta días posteriores a la recepción por parte del trabajador de la notificación de desplazamiento, en los otros países mencionados no existen limitaciones específicas al ejercicio de este derecho.

http://ec.europa.eu/employment_social/social_security_scheme...
La obligación de cotizar cesa cuando el afiliado alcanza la edad de jubilación (65 años).Sin embargo, en caso de que haya alcanzado la edad requerida pero no cumpla las condiciones de cotización que dan derecho a la pensión de vejez, deberá continuar cotizando hasta que las cumpla.
http://ec.europa.eu/employment_social/social_security_scheme...
The obligation to pay contributions ceases when the insured person reaches pensionable age (65 years). However, if he has reached the required age but does not satisfy the contribution conditions entitling him to old-age pension, he must continue to contribute until the conditions are satisfied.

I understand it to mean 'keep in effect', with 'coverage/ benefits/ protection' implied. However, it doesn't make sense in English unless you specify the object. If you don't specify the object, the English text will imply a commitment to keep the social security system itself in effect, which is not what is meant.

The whole thing would be:

"preserve/guarantee social security benefits and continue making contributions to the system in the host country "